Touch determination by tomographic reconstruction

ABSTRACT

A touch-sensitive apparatus comprises a panel configured to conduct signals from a plurality of peripheral incoupling points to a plurality of peripheral outcoupling points. Actual detection lines are defined between pairs of incoupling and outcoupling points to extend across a surface portion of the panel. The signals may be in the form of light, and objects touching the surface portion may affect the light via frustrated total internal reflection (FTIR). A signal generator is coupled to the incoupling points to generate the signals, and a signal detector is coupled to the outcoupling points to generate an output signal. A data processor operates on the output signal to enable identification of touching objects. The output signal is processed ( 40 ) to generate a set of data samples, which are indicative of detected energy for at least a subset of the actual detection lines. The set of data samples is processed ( 42 ) to generate a set of matched samples, which are indicative of estimated detected energy for fictitious detection lines that have a location on the surface portion that matches a standard geometry for tomographic reconstruction. The set of matched samples is processed ( 44, 46 ) by tomographic reconstruction to generate data indicative of a distribution of an energy-related parameter within at least part of the surface portion.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a Continuation application of U.S. Ser. No.13/695,505, filed Oct. 31, 2012, which is a National Phase Applicationof PCT/SE2011/050520, filed Apr. 28, 2011, which claims the benefit ofSwedish patent application No. 1050434-8, filed on May 3, 2010, Swedishpatent application No. 1051062-6, filed on Oct. 11, 2010, and U.S.provisional application No. 61/282,973, filed on May 3, 2010, all ofwhich are incorporated herein by reference.

TECHNICAL FIELD

The present invention relates to touch-sensitive panels and dataprocessing techniques in relation to such panels.

BACKGROUND ART

To an increasing extent, touch-sensitive panels are being used forproviding input data to computers, electronic measurement and testequipment, gaming devices, etc. The panel may be provided with agraphical user interface (GUI) for a user to interact with using e.g. apointer, stylus or one or more fingers. The GUI may be fixed or dynamic.A fixed GUI may e.g. be in the form of printed matter placed over, underor inside the panel. A dynamic GUI can be provided by a display screenintegrated with, or placed underneath, the panel or by an image beingprojected onto the panel by a projector.

There are numerous known techniques for providing touch sensitivity tothe panel, e.g. by using cameras to capture light scattered off thepoint(s) of touch on the panel, or by incorporating resistive wiregrids, capacitive sensors, strain gauges, etc into the panel.

US2004/0252091 discloses an alternative technique which is based onfrustrated total internal reflection (FTIR). Light sheets are coupledinto a panel to propagate inside the panel by total internal reflection.When an object comes into contact with a surface of the panel, two ormore light sheets will be locally attenuated at the point of touch.Arrays of light sensors are located around the perimeter of the panel todetect the received light for each light sheet. A coarse tomographicreconstruction of the light field across the panel surface is thencreated by geometrically back-tracing and triangulating all attenuationsobserved in the received light. This is stated to result in dataregarding the position and size of each contact area.

US2009/0153519 discloses a panel capable of conducting signals. A“tomograph” is positioned adjacent the panel with signal flow portsarrayed around the border of the panel at discrete locations. Signals(b) measured at the signal flow ports are tomographically processed togenerate a two-dimensional representation (x) of the conductivity on thepanel, whereby touching objects on the panel surface can be detected.The presented technique for tomographic reconstruction is based on alinear model of the tomographic system, Ax=b. The system matrix A iscalculated at factory, and its pseudo inverse A⁻¹ is calculated usingTruncated SVD algorithms and operated on the measured signals to yieldthe two-dimensional (2D) representation of the conductivity: x=A⁻¹b. Thesuggested method is both demanding in the term of processing and lackssuppression of high frequency components, possibly leading to much noisein the 2D representation.

US2009/0153519 also makes a general reference to Computer Tomography(CT). CT methods are well-known imaging methods which have beendeveloped for medical purposes. CT methods employ digital geometryprocessing to reconstruct an image of the inside of an object based on alarge series of projection measurements through the object. Various CTmethods have been developed to enable efficient processing and/orprecise image reconstruction, e.g. Filtered Back Projection, ART, SART,etc. Often, the projection measurements are carried out in accordancewith a standard geometry which is given by the CT method. Clearly, itwould be desirable to capitalize on existing CT methods forreconstructing the 2D distribution of an energy-related parameter(light, conductivity, etc) across a touch surface based on a set ofprojection measurements.

SUMMARY

It is an object of the invention to enable touch determination on apanel based on projection measurements by use of existing CT methods.

Another objective is to provide a technique that enables determinationof touch-related data at sufficient precision to discriminate between aplurality of objects in simultaneous contact with a touch surface.

This and other objects, which may appear from the description below, areat least partly achieved by means of a method of enabling touchdetermination, a computer program product, a device for enabling touchdetermination, and a touch-sensitive apparatus according to theindependent claims, embodiments thereof being defined by the dependentclaims.

A first aspect of the invention is a method of enabling touchdetermination based on an output signal from a touch-sensitiveapparatus, which comprises a panel configured to conduct signals from aplurality of peripheral incoupling points to a plurality of peripheraloutcoupling points, thereby defining actual detection lines that extendacross a surface portion of the panel between pairs of incoupling andoutcoupling points, at least one signal generator coupled to theincoupling points to generate the signals, and at least one signaldetector coupled to the outcoupling points to generate the outputsignal. The method comprises: processing the output signal to generate aset of data samples, wherein the data samples are indicative of detectedenergy for at least a subset of the actual detection lines; processingthe set of data samples to generate a set of matched samples, whereinthe matched samples are indicative of estimated detected energy forfictitious detection lines that have a location on the surface portionthat matches a standard geometry for tomographic reconstruction; andprocessing the set of matched samples by tomographic reconstruction togenerate data indicative of a distribution of an energy-relatedparameter within at least part of the surface portion.

In one embodiment, the step of processing the output signal comprises:generating the data samples in a two-dimensional sample space, whereineach data sample is representative of an actual detection line and isdefined by a signal value and two dimension values that define thelocation of the actual detection line on the surface portion.

In one embodiment, the step of processing the set of data samplescomprises: generating estimated signal values of the matched samples atpredetermined locations in the two-dimensional sample space, wherein thepredetermined locations correspond to the fictitious detection lines.The estimated signal values may be generated by interpolation based onthe signal values of the data samples, and each estimated signal valuemay be generated by interpolation of the signal values of neighboringdata samples in the two-dimensional sample space.

In one embodiment, the step of processing the set of data samplesfurther comprises: obtaining a predetermined two-dimensionalinterpolation function with nodes corresponding to the set of datasamples, and calculating the estimated signal values according to theinterpolation function and based on the signal values of the datasamples. The method may further comprise a step of receiving exclusiondata identifying one or more data samples to be excluded, wherein thestep of processing the data samples comprises identifying the nodecorresponding to each data sample to be excluded, re-designing thepredetermined interpolation function without each thus-identified node,and calculating the estimated signal values according to the re-designedinterpolation scheme and based on the signal values of the data samplesin the nodes of the re-designed interpolation scheme.

In one embodiment, the step of generating estimated signal valuescomprises, for each matched sample: calculating a weighted contributionto the matched sample from at least a subset of the data samples, andaggregating the weighted contributions, wherein each weightedcontribution is calculated as a function of the signal value of the datasample and a distance in the sample space between the matched sample andthe data sample.

In one embodiment, the matched samples are arranged as rows and/orcolumns in the two-dimensional sample space. The matched samples may bearranged with equidistant spacing within each of said rows and/orcolumns.

In an alternative embodiment, the step of processing the set of datasamples comprises: operating a two-dimensional Fourier transformationalgorithm designed for irregularly sampled data on the set of datasamples to generate a set of Fourier coefficients arranged in aCartesian grid; and generating the estimated signal values by operatinga two-dimensional inverse FFT algorithm on the set of Fouriercoefficients to generate the set of matched samples.

In one embodiment, the step of processing the set of matched samplescomprises: applying a one-dimensional high-pass filtering of the matchedsamples in the two-dimensional sample space to generate filteredsamples, and processing the filtered samples to generate at set of backprojection values indicative of said distribution.

In one embodiment, the surface portion defines a sampling area in thetwo-dimensional sample space, and the step of processing comprises, ifthe actual detection lines given by the geometric arrangement ofincoupling and outcoupling points result in at least one contiguousregion without data samples within the sampling area, the steps of:obtaining a predetermined set of estimated sampling points within thecontiguous region, and, for each estimated sampling point, identifyingthe location of a corresponding fictitious detection line on the surfaceportion; identifying, for each intersection point between thecorresponding fictitious detection line and the actual detection linesand/or between the corresponding fictitious detection line and thefictitious detection lines for the set of matched samples, anintersection point value as the smallest signal value of all datasamples corresponding to the actual detection lines associated with theintersection point; and calculating a signal value of the estimatedsampling point as a function of the intersection point values. In oneimplementation, the signal value of the estimated sampling point may begiven by the largest intersection point value. In anotherimplementation, the method further comprises, for each estimatedsampling point: identifying a number of local maxima in the intersectionpoint values, and calculating the signal value of the estimated samplingpoint as a combination of the local maxima.

In one embodiment, the dimension values comprise a rotation angle of thedetection line in the plane of the panel, and a distance of thedetection line in the plane of the panel from a predetermined origin.

In another embodiment, the dimension values comprise an angular locationof the incoupling or outcoupling point of the detection line, and arotation angle of the detection line in the plane of the panel. In oneimplementation, the standard geometry is a fan geometry, the touchsurface has a non-circular perimeter, and the angular location isdefined by an intersection between the detection line and a fictitiouscircle arranged to circumscribe the touch surface.

In one embodiment, the standard geometry is one of a parallel geometryand a fan geometry.

In one embodiment, the signals comprise one of electrical energy, light,magnetic energy, sonic energy and vibration energy.

In one embodiment, the panel defines a touch surface and an oppositesurface, wherein said at least one signal generator is arranged toprovide light inside the panel, such that the light propagates from theincoupling points by internal reflection between the touch surface andthe opposite surface to the outcoupling points for detection by said atleast one signal detector, and wherein the touch-sensitive apparatus isconfigured such that the propagating light is locally attenuated by oneor more objects touching the touch surface.

A second aspect of the invention is a computer program productcomprising computer code which, when executed on a data-processingsystem, is adapted to carry out the method of the first aspect.

A third aspect of the invention is a device for enabling touchdetermination based on an output signal of a touch-sensitive apparatus,which comprises a panel configured to conduct signals from a pluralityof peripheral incoupling points to a plurality of peripheral outcouplingpoints, thereby defining actual detection lines that extend across asurface portion of the panel between pairs of incoupling and outcouplingpoints, means for generating the signals at the incoupling points, andmeans for generating the output signal based on detected signals at theoutcoupling points. The device comprises: means for receiving the outputsignal; means for processing the output signal to generate a set of datasamples, wherein the data samples are indicative of detected energy forat least a subset of the actual detection lines; means for processingthe set of data samples to generate a set of matched samples, whereinthe matched samples are indicative of estimated detected energy forfictitious detection lines that have a location on the surface portionthat matches a standard geometry for tomographic reconstruction; andmeans for processing the set of matched samples by tomographicreconstruction to generate data indicative of a distribution of anenergy-related parameter within at least part of the surface portion.

A fourth aspect of the invention is a touch-sensitive apparatus,comprising: a panel configured to conduct signals from a plurality ofperipheral incoupling points to a plurality of peripheral outcouplingpoints, thereby defining actual detection lines that extend across asurface portion of the panel between pairs of incoupling and outcouplingpoints; means for generating the signals at the incoupling points; meansfor generating an output signal based on detected signals at theoutcoupling points; and the device for enabling touch determinationaccording to the third aspect.

A fifth aspect of the invention is a touch-sensitive apparatus,comprising: a panel configured to conduct signals from a plurality ofperipheral incoupling points to a plurality of peripheral outcouplingpoints, thereby defining actual detection lines that extend across asurface portion of the panel between pairs of incoupling and outcouplingpoints; at least one signal generator coupled to the incoupling pointsto generate the signals; at least one signal detector coupled to theoutcoupling points to generate an output signal; and a signal processorconnected to receive the output signal and configured to: process theoutput signal to generate a set of data samples, wherein the datasamples are indicative of detected energy for at least a subset of theactual detection lines, process the set of data samples to generate aset of matched samples, wherein the matched samples are indicative ofestimated detected energy for fictitious detection lines that have alocation on the surface portion that matches a standard geometry fortomographic reconstruction, and process the set of matched samples bytomographic reconstruction to generate data indicative of a distributionof an energy-related parameter within at least part of the surfaceportion.

Any one of the embodiments of the first aspect can be combined with thesecond to fifth aspects.

Still other objectives, features, aspects and advantages of the presentinvention will appear from the following detailed description, from theattached claims as well as from the drawings.

BRIEF DESCRIPTION OF DRAWINGS

Embodiments of the invention will now be described in more detail withreference to the accompanying schematic drawings.

FIG. 1 is a plan view of a touch-sensitive apparatus.

FIG. 2A-2B are top plan views of a touch-sensitive apparatus with aninterleaved and non-interleaved arrangement, respectively, of emittersand sensors.

FIGS. 3A-3B are side and top plan views of touch-sensitive systemsoperating by frustrated total internal reflection (FTIR).

FIG. 4A is a flow chart of a reconstruction method, and FIG. 4B is ablock diagram of a device that implements the method of FIG. 4A.

FIG. 5 illustrates the underlying principle of the Projection-SliceTheorem.

FIG. 6 illustrates the applicability of filtering for back projectionprocessing.

FIG. 7 illustrates a parallel geometry used in tomographicreconstruction.

FIGS. 8A-8H illustrate a starting point, intermediate results and finalresults of a back projection process using a parallel geometry.

FIG. 9 illustrates a fan geometry used in tomographic reconstruction.

FIGS. 10A-10C illustrate intermediate and final results of a backprojection process using a fan geometry.

FIG. 11 is graph of projection values collected in the fan geometry ofFIG. 9 mapped to a sampling space for a parallel geometry.

FIG. 12A is a graph of sampling points defined by interleavedarrangement in FIG. 2A, FIGS. 12B-12C illustrate discrepancies betweendetection lines in an interleaved arrangement and a fan geometry, andFIG. 12D is a graph of sampling points for the non-interleavedarrangement in FIG. 2B.

FIG. 13 is a reference image mapped to an interleaved arrangement.

FIG. 14A is a graph of a 2D interpolation function for an interleavedarrangement, FIG. 14B illustrates the generation of interpolation pointsusing the interpolation function of FIG. 14A, FIG. 14C is aninterpolated sinogram generated based on the reference image in FIG. 13,and FIG. 14D is a reconstructed attenuation field.

FIGS. 15A-15D and FIGS. 16A-16B illustrate how the 2D interpolationfunction is updated when sampling points are removed fromreconstruction.

FIG. 17 is a reference image mapped to a non-interleaved arrangement.

FIGS. 18A-18B illustrate a first variant for reconstruction in anon-interleaved arrangement.

FIGS. 19A-19B illustrate a second variant for reconstruction in anon-interleaved arrangement.

FIGS. 20A-20B illustrate a third variant for reconstruction in anon-interleaved arrangement.

FIGS. 21A-21B illustrate a fourth variant for reconstruction in anon-interleaved arrangement.

FIGS. 22A-22F illustrate a fifth variant for reconstruction in anon-interleaved arrangement.

FIGS. 23A-23E illustrate a sixth variant for reconstruction in anon-interleaved arrangement.

FIG. 24 is a flowchart of a process for filtered back projection.

FIGS. 25A-25B illustrate a first variant for reconstruction in aninterleaved arrangement using a tomographic algorithm designed for fangeometry.

FIGS. 26A-26B illustrate a second variant for reconstruction in aninterleaved arrangement using a tomographic algorithm designed for fangeometry.

FIG. 27 illustrates the use of a circle for defining a two-dimensionalsample space of a touch-sensitive apparatus.

FIG. 28A-28D illustrate a third variant for reconstruction in aninterleaved arrangement using a tomographic algorithm designed for fangeometry.

FIG. 29 shows the reconstructed attenuation field in FIG. 22F afterimage enhancement processing.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

The present invention relates to techniques for enabling extraction oftouch data for at least one object, and typically multiple objects, incontact with a touch surface of a touch-sensitive apparatus. Thedescription starts out by presenting the underlying concept of such atouch-sensitive apparatus, especially an apparatus operating byfrustrated total internal reflection (FTIR) of light. Then follows anexample of an overall method for touch data extraction involvingtomographic reconstruction. The description continues to generallyexplain and exemplify the theory of tomographic reconstruction and itsuse of standard geometries. Finally, different inventive aspects ofapplying techniques for tomographic reconstruction for touchdetermination are further explained and exemplified.

Throughout the description, the same reference numerals are used toidentify corresponding elements.

1. Touch-Sensitive Apparatus

FIG. 1 illustrates a touch-sensitive apparatus 100 which is based on theconcept of transmitting energy of some form across a touch surface 1,such that an object that is brought into close vicinity of, or incontact with, the touch surface 1 causes a local decrease in thetransmitted energy. The touch-sensitive apparatus 100 includes anarrangement of emitters and sensors, which are distributed along theperiphery of the touch surface. Each pair of an emitter and a sensordefines a detection line, which corresponds to the propagation path foran emitted signal from the emitter to the sensor. In FIG. 1, only onesuch detection line D is illustrated to extend from emitter 2 to sensor3, although it should be understood that the arrangement typicallydefines a dense grid of intersecting detection lines, each correspondingto a signal being emitted by an emitter and detected by a sensor. Anyobject that touches the touch surface along the extent of the detectionline D will thus decrease its energy, as measured by the sensor 3.

The arrangement of sensors is electrically connected to a signalprocessor 10, which samples and processes an output signal from thearrangement. The output signal is indicative of the received energy ateach sensor 3. As will be explained below, the signal processor 10 maybe configured to process the output signal by a tomographic technique torecreate an image of the distribution of an energy-related parameter(for simplicity, referred to as “energy distribution” in the following)across the touch surface 1. The energy distribution may be furtherprocessed by the signal processor 10 or by a separate device (not shown)for touch determination, which may involve extraction of touch data,such as a position (e.g. x, y coordinates), a shape or an area of eachtouching object.

In the example of FIG. 1, the touch-sensitive apparatus 100 alsoincludes a controller 12 which is connected to selectively control theactivation of the emitters 2. The signal processor 10 and the controller12 may be configured as separate units, or they may be incorporated in asingle unit. One or both of the signal processor 10 and the controller12 may be at least partially implemented by software executed by aprocessing unit.

The touch-sensitive apparatus 100 may be designed to be used with adisplay device or monitor, e.g. as described in the Background section.Generally, such a display device has a rectangular extent, and thus thetouch-sensitive apparatus 100 (the touch surface 1) is also likely to bedesigned with a rectangular shape. Further, the emitters 2 and sensors 3all have a fixed position around the perimeter of the touch surface 1.Thus, in contrast to a conventional tomographic apparatus used e.g. inthe medical field, there will be no possibility of rotating the completemeasurement system. As will be described in further detail below, thisputs certain limitations on the use of standard tomographic techniquesfor recreating/reconstructing the energy distribution within the touchsurface 1.

In the following, embodiments of the invention will be described inrelation to two main arrangements of emitters 2 and sensors 3. A firstmain arrangement, shown in FIG. 2A, is denoted “interleaved arrangement”and has emitters 2 and sensors 3 placed one after the other along theperiphery of the touch surface 1. Thus, every emitter 2 is placedbetween two sensors 3. The distance between neighboring emitters 2 isthe same along the periphery. The same applies for the distance betweenneighboring sensors 3. A second main arrangement, shown in FIG. 2B, isdenoted “non-interleaved arrangement” and has merely sensors 3 on twoadjacent sides (i.e. sides connected via a corner), and merely emitters2 on its other sides.

The interleaved arrangement may be preferable since it generates a moreuniform distribution of detection lines. However, there areelectro-optical aspects of the interleaved system that may favor the useof the non-interleaved arrangement. For example, the interleavedarrangement may require the emitters 2, which may be fed with highdriving currents, to be located close to the sensors 3, which areconfigured to detect weak photo-currents. This may lead to undesireddetection noise. The electrical connection to the emitters 2 and sensors3 may also be somewhat demanding since the emitters 2 and sensors 3 aredispersed around the periphery of the touch surface 1. Thus, there maybe reasons for using a non-interleaved arrangement instead of aninterleaved arrangement, since the former obviates these potentialobstacles.

It is to be understood that there are many variations and blends ofthese two types of arrangements. For example, the sensor-sensor,sensor-emitter, emitter-emitter distance(s) may vary along theperiphery, and/or the blending of emitters and sensors may be different,e.g. there may be two or more emitters/sensors between everyemitter/sensor, etc. Although the following examples are given for thefirst and second main arrangements, specifically a rectangular touchsurface with a 16:9 aspect ratio, this is merely for the purpose ofillustration, and the concepts of the invention are applicableirrespective of aspect ratio, shape of the touch surface, andarrangement of emitters and sensors.

In the embodiments shown herein, at least a subset of the emitters 2 maybe arranged to emit energy in the shape of a beam or wave that divergesin the plane of the touch surface 1, and at least a subset of thesensors 3 may be arranged to receive energy over a wide range of angles(field of view). Alternatively or additionally, the individual emitter 2may be configured to emit a set of separate beams that propagate to anumber of sensors 3. In either embodiment, each emitter 2 transmitsenergy to a plurality of sensors 3, and each sensor 3 receives energyfrom a plurality of emitters 2.

The touch-sensitive apparatus 100 may be configured to permittransmission of energy in one of many different forms. The emittedsignals may thus be any radiation or wave energy that can travel in andacross the touch surface 1 including, without limitation, light waves inthe visible or infrared or ultraviolet spectral regions, electricalenergy, electromagnetic or magnetic energy, or sonic and ultrasonicenergy or vibration energy.

In the following, an example embodiment based on propagation of lightwill be described. FIG. 3A is a side view of a touch-sensitive apparatus100 which includes a light transmissive panel 4, one or more lightemitters 2 (one shown) and one or more light sensors 3 (one shown). Thepanel 4 defines two opposite and generally parallel surfaces 5, 6 andmay be planar or curved. A radiation propagation channel is providedbetween two boundary surfaces 5, 6 of the panel 4, wherein at least oneof the boundary surfaces allows the propagating light to interact with atouching object 7. Typically, the light from the emitter(s) 2 propagatesby total internal reflection (TIR) in the radiation propagation channel,and the sensors 3 are arranged at the periphery of the panel 4 togenerate a respective measurement signal which is indicative of theenergy of received light.

As shown in FIG. 3A, the light may be coupled into and out of the panel4 directly via the edge portion that connects the top and bottomsurfaces 5, 6 of the panel 4. Alternatively, not shown, a separatecoupling element (e.g. in the shape of a wedge) may be attached to theedge portion or to the top or bottom surface 5, 6 of the panel 4 tocouple the light into and/or out of the panel 4. When the object 7 isbrought sufficiently close to the boundary surface, part of the lightmay be scattered by the object 7, part of the light may be absorbed bythe object 7, and part of the light may continue to propagateunaffected. Thus, when the object 7 touches a boundary surface of thepanel (e.g. the top surface 5), the total internal reflection isfrustrated and the energy of the transmitted light is decreased. Thistype of touch-sensitive apparatus is denoted “FTIR system”(FTIR—Frustrated Total Internal Reflection) in the following.

The touch-sensitive apparatus 100 may be operated to measure the energyof the light transmitted through the panel 4 on a plurality of detectionlines. This may, e.g., be done by activating a set of spaced-apartemitters 2 to generate a corresponding number of light sheets inside thepanel 4, and by operating a set of sensors 3 to measure the transmittedenergy of each light sheet. Such an embodiment is illustrated in FIG.3B, where each emitter 2 generates a beam of light that expands in theplane of the panel 4 while propagating away from the emitter 2. Eachbeam propagates from one or more entry or incoupling points within anincoupling site on the panel 4. Arrays of light sensors 3 are locatedaround the perimeter of the panel 4 to receive the light from theemitters 2 at a number of spaced-apart outcoupling points within anoutcoupling site on the panel 4. It should be understood that theincoupling and outcoupling points merely refer to the position where thebeam enters and leaves, respectively, the panel 4. Thus, oneemitter/sensor may be optically coupled to a number ofincoupling/outcoupling points. In the example of FIG. 3B, however, thedetection lines D are defined by individual emitter-sensor pairs.

The light sensors 3 collectively provide an output signal, which isreceived and sampled by the signal processor 10. The output signalcontains a number of sub-signals, also denoted “projection signals”,each representing the energy of light emitted by a certain light emitter2 and received by a certain light sensor 3, i.e. the received energy ona certain detection line. Depending on implementation, the signalprocessor 10 may need to process the output signal for identification ofthe individual sub-signals. Irrespective of implementation, the signalprocessor 10 is able to obtain an ensemble of measurement values thatcontains information about the distribution of an energy-relatedparameter across the touch surface 1.

The light emitters 2 can be any type of device capable of emitting lightin a desired wavelength range, for example a diode laser, a VCSEL(vertical-cavity surface-emitting laser), or alternatively an LED(light-emitting diode), an incandescent lamp, a halogen lamp, etc.

The light sensors 3 can be any type of device capable of detecting theenergy of light emitted by the set of emitters, such as a photodetector,an optical detector, a photo-resistor, a photovoltaic cell, aphotodiode, a reverse-biased LED acting as photodiode, a charge-coupleddevice (CCD) etc.

The emitters 2 may be activated in sequence, such that the receivedenergy is measured by the sensors 3 for each light sheet separately.Alternatively, all or a subset of the emitters 2 may be activatedconcurrently, e.g. by modulating the emitters 2 such that the lightenergy measured by the sensors 3 can be separated into the sub-signalsby a corresponding de-modulation.

Reverting to the emitter-sensor-arrangements in FIG. 2, the spacingbetween neighboring emitters 2 and sensors 3 in the interleavedarrangement (FIG. 2A) and between neighboring emitters 2 and neighboringsensors 3, respectively, in the non-interleaved arrangement (FIG. 2B) isgenerally from about 1 mm to about 20 mm. For practical as well asresolution purposes, the spacing is generally in the 2-10 mm range.

In a variant of the interleaved arrangement, the emitters 2 and sensors3 may partially or wholly overlap, as seen in a plan view. This can beaccomplished by placing the emitters 2 and sensors 3 on opposite sidesof the panel 4, or in some equivalent optical arrangement.

It is to be understood that FIG. 3 merely illustrates one example of anFTIR system. Further examples of FTIR systems are e.g. disclosed in U.S.Pat. No. 6,972,753, U.S. Pat. No. 7,432,893, US2006/0114237,US2007/0075648, WO2009/048365, WO2010/006882, WO2010/006883,WO2010/006884, WO2010/006885, WO2010/006886, and Internationalapplication No. PCT/SE2009/051364, which are all incorporated herein bythis reference. The inventive concept may be advantageously applied tosuch alternative FTIR systems as well.

2. Transmission

As indicated in FIG. 3A, the light will not be blocked by the touchingobject 7. Thus, if two objects 7 happen to be placed after each otheralong a light path from an emitter 2 to a sensor 3, part of the lightwill interact with both objects 7. Provided that the light energy issufficient, a remainder of the light will reach the sensor 3 andgenerate an output signal that allows both interactions (touch points)to be identified. Thus, in multi-touch FTIR systems, the transmittedlight may carry information about a plurality of touches.

In the following, T_(j) is the transmission for the j:th detection line,T_(y) is the transmission at a specific position along the detectionline, and A_(v) is the relative attenuation at the same point. The totaltransmission (modeled) along a detection line is thus:

$T_{j} = {{\prod\limits_{v}T_{v}} = {\prod\limits_{v}\left( {1 - A_{v}} \right)}}$

The above equation is suitable for analyzing the attenuation caused bydiscrete objects on the touch surface, when the points are fairly largeand separated by a distance. However, a more correct definition ofattenuation through an attenuating medium may be used:I _(j) =I _(0,j) ·e ^(−∫a(x)dx) →T _(j) =I _(j) /I _(0,j) =e ^(−∫a(x)dx)

In this formulation, I_(j) represents the transmitted energy ondetection line D_(j) with attenuating object(s), I_(0,j) represents thetransmitted energy on detection line D_(j) without attenuating objects,and a(x) is the attenuation coefficient along the detection line D_(j).We also let the detection line interact with the touch surface along theentire extent of the detection line, i.e. the detection line isrepresented as a mathematical line.

To facilitate the tomographic reconstruction as described in thefollowing, the measurement values may be divided by a respectivebackground value. By proper choice of background values, the measurementvalues are thereby converted into transmission values, which thusrepresent the fraction of the available light energy that has beenmeasured on each of the detection lines.

The theory of the Radon transform (see below) deals with line integrals,and it may therefore be proper to use the logarithm of the aboveexpression:log(T)=log(e ^(−∫a(x)dx))=−∫a(x)dx3. Reconstruction and Touch Data Extraction

FIG. 4A illustrates an embodiment of a method for reconstruction andtouch data extraction in an FTIR system. The method involves a sequenceof steps 40-48 that are repeatedly executed, typically by the signalprocessor 10 (FIGS. 1 and 3). In the context of this description, eachsequence of steps 40-48 is denoted a sensing instance.

Each sensing instance starts by a data collection step 40, in whichmeasurement values are sampled from the light sensors 3 in the FTIRsystem, typically by sampling a value from each of the aforesaidsub-signals. The data collection results in one projection value foreach detection line. It may be noted that the data may, but need not, becollected for all available detection lines in the FTIR system. The datacollection step 40 may also include pre-processing of the measurementvalues, e.g. filtering for noise reduction, conversion of measurementvalues into transmission values (or equivalently, attenuation values),conversion into logarithmic values, etc.

In a re-calculation step 42, the set of projection values are processedfor generation of an updated set of projection values that representfictitious detection lines with a location on the touch surface thatmatches a standard geometry for tomographic reconstruction. This steptypically involves an interpolation among the projection values aslocated in a 2D sample space which is defined by two dimensions thatrepresent the unique location of the detection lines on the touchsurface. In this context, a “location” refers to the physical extent ofthe detection line on the touch surface as seen in a plan view. There-calculation step 42 will be further explained and motivated inChapter 6 below.

In a filtering step 44, the updated set of projection values issubjected to a filtering aiming at increasing high spatial frequenciesin relation to low spatial frequencies amongst the set of projectionvalues. Thus, step 44 results in a filtered version of the updated setof projection values, denoted “filtered set” in the following.Typically, step 44 involves applying a suitable 1D filter kernel to theupdated set of projection values. The use of filter kernels will befurther explained and motivated in Chapter 4 below. In certainembodiments, it may be advantageous to apply a low-pass filter to theupdated set of projection values before applying the 1D filter kernel.

In a reconstruction step 46, an “attenuation field” across the touchsurface is reconstructed by processing the filtered set in the 2D samplespace. The attenuation field is a distribution of attenuation valuesacross the touch surface (or a relevant part of the touch surface), i.e.an energy-related parameter. As used herein, “the attenuation field” and“attenuation values” may be given in terms of an absolute measure, suchas light energy, or a relative measure, such as relative attenuation(e.g. the above-mentioned attenuation coefficient) or relativetransmission. Step 46 may involve applying a back projection operator tothe filtered set of projection values in the 2D sample space. Such anoperator typically generates an individual attenuation value bycalculating some form of weighted sum of selected projection valuesincluded the filtered set. The use of a back projection operator will befurther explained and motivated in Chapters 4 and 5 below.

The attenuation field may be reconstructed within one or more subareasof the touch surface. The subareas may be identified by analyzingintersections of detection lines across the touch surface, based on theabove-mentioned projection signals. Such a technique for identifyingsubareas is further disclosed in Applicant's U.S. provisional patentapplication No. 61/272,665, which was filed on Oct. 19, 2009 and whichis incorporated herein by this reference.

In a subsequent extraction step 48, the reconstructed attenuation fieldis processed for identification of touch-related features and extractionof touch data. Any known technique may be used for isolating true(actual) touch points within the attenuation field. For example,ordinary blob detection and tracking techniques may be used for findingthe actual touch points. In one embodiment, a threshold is first appliedto the attenuation field, to remove noise. Any areas with attenuationvalues that exceed the threshold, may be further processed to find thecenter and shape by fitting for instance a two-dimensional second-orderpolynomial or a Gaussian bell shape to the attenuation values, or byfinding the ellipse of inertia of the attenuation values. There are alsonumerous other techniques as is well known in the art, such asclustering algorithms, edge detection algorithms, etc.

Any available touch data may be extracted, including but not limited tox,y coordinates, areas, shapes and/or pressure of the touch points.

After step 48, the extracted touch data is output, and the processreturns to the data collection step 40.

It is to be understood that one or more of steps 40-48 may be effectedconcurrently. For example, the data collection step 40 of a subsequentsensing instance may be initiated concurrently with any of steps 42-48.In can also be noted that the re-calculation and filtering steps 42, 44can be merged into one single step, since these steps generally involvelinear operations.

The touch data extraction process is typically executed by a dataprocessing device (cf. signal processor 10 in FIGS. 1 and 3) which isconnected to sample the measurement values from the light sensors 3 inthe FTIR system. FIG. 4B shows an example of such a data processingdevice 10 for executing the process in FIG. 4A. In the illustratedexample, the device 10 includes an input 400 for receiving the outputsignal. The device 10 further includes a data collection element (ormeans) 402 for processing the output signal to generate theabove-mentioned set of projection values, and a re-calculation element(or means) 404 for generating the above-mentioned updated set ofprojection values. There is also provided a filtering element (or means)406 for generating the above-mentioned filtered set. The device 10further includes a reconstruction element (or means) 408 for generatingthe reconstructed attenuation field by processing the filtered set, andan output 410 for outputting the reconstructed attenuation field. In theexample of FIG. 4B, the actual extraction of touch data is carried outby a separate device 10′ which is connected to receive the attenuationfield from the data processing device 10.

The data processing device 10 may be implemented by special-purposesoftware (or firmware) run on one or more general-purpose orspecial-purpose computing devices. In this context, it is to beunderstood that each “element” or “means” of such a computing devicerefers to a conceptual equivalent of a method step; there is not alwaysa one-to-one correspondence between elements/means and particular piecesof hardware or software routines. One piece of hardware sometimescomprises different means/elements. For example, a processing unitserves as one element/means when executing one instruction, but servesas another element/means when executing another instruction. Inaddition, one element/means may be implemented by one instruction insome cases, but by a plurality of instructions in some other cases. Sucha software controlled computing device may include one or moreprocessing units, e.g. a CPU (“Central Processing Unit”), a DSP(“Digital Signal Processor”), an ASIC (“Application-Specific IntegratedCircuit”), discrete analog and/or digital components, or some otherprogrammable logical device, such as an FPGA (“Field Programmable GateArray”). The data processing device 10 may further include a systemmemory and a system bus that couples various system components includingthe system memory to the processing unit. The system bus may be any ofseveral types of bus structures including a memory bus or memorycontroller, a peripheral bus, and a local bus using any of a variety ofbus architectures. The system memory may include computer storage mediain the form of volatile and/or non-volatile memory such as read onlymemory (ROM), random access memory (RAM) and flash memory. Thespecial-purpose software may be stored in the system memory, or on otherremovable/non-removable volatile/non-volatile computer storage mediawhich is included in or accessible to the computing device, such asmagnetic media, optical media, flash memory cards, digital tape, solidstate RAM, solid state ROM, etc. The data processing device 10 mayinclude one or more communication interfaces, such as a serialinterface, a parallel interface, a USB interface, a wireless interface,a network adapter, etc, as well as one or more data acquisition devices,such as an A/D converter. The special-purpose software may be providedto the data processing device 10 on any suitable computer-readablemedium, including a record medium, a read-only memory, or an electricalcarrier signal.

4. Tomographic Techniques

Tomographic reconstruction, which is well-known per se, may be based onthe mathematics describing the Radon transform and its inverse. Thefollowing theoretical discussion is limited to the 2D Radon transform.The general concept of tomography is to do imaging of a medium bymeasuring line integrals through the medium for a large set of anglesand positions. The line integrals are measured through the image plane.To find the inverse, i.e. the original image, many algorithms use theso-called Projection-Slice Theorem.

Several efficient algorithms have been developed for tomographicreconstruction, e.g. Filtered Back Projection (FBP), FFT-basedalgorithms, ART (Algebraic Reconstruction Technique), SART (SimultaneousAlgebraic Reconstruction Technique), etc. Filtered Back Projection is awidely used algorithm, and there are many variants and extensionsthereof. Below, a brief outline of the underlying mathematics for FBP isgiven, for the sole purpose of facilitating the following discussionabout the inventive concept and its merits.

4.1 Projection-Slice Theorem

Many tomographic reconstruction techniques make use of a mathematicaltheorem called Projection-Slice Theorem. This Theorem states that givena two-dimensional function ƒ(x,y), the one- and two-dimensional Fouriertransforms

₁ and

₂, a projection operator

that projects a two-dimensional (2D) function onto a one-dimensional(1D) line, and a slice operator S₁ that extracts a central slice of afunction, the following calculations are equal:

₁

f(x,y)=S ₁

₂ f(x,y)

This relation is illustrated in FIG. 5. The right-hand side of theequation above essentially extracts a 1D line of the 2D Fouriertransform of the function ƒ(x,y). The line passes through the origin ofthe 2D Fourier plane, as shown in the right-hand part of FIG. 5. Theleft-hand side of the equation starts by projecting (i.e. integratingalong 1D lines in the projection direction p) the 2D function onto a 1Dline (orthogonal to the projection direction p), which forms a“projection” that is made up of the projection values for all thedifferent detection lines extending in the projection direction p. Thus,taking a 1D Fourier transform of the projection gives the same result astaking a slice from the 2D Fourier transform of the function ƒ(x,y). Inthe context of the present disclosure, the function ƒ(x,y) correspondsto the attenuation coefficient field a(x) (generally denoted“attenuation field” herein) to be reconstructed.

4.2 Radon Transform

First, it can be noted that the attenuation vanishes outside the touchsurface. For the following mathematical discussion, we define a circulardisc that circumscribes the touch surface, Ω_(r)={x:|x|≦r}, with theattenuation field set to zero outside of this disc. Further, theprojection value for a given detection line is given by:

g(θ, s) = ( a)(θ, s) = ∫_(s = x ⋅ θ)a(x)𝕕x

Here, we let θ=(cos φ, sin φ) be a unit vector denoting the directionnormal to the detection line, and s is the shortest distance (with sign)from the detection line to the origin (taken as the centre of thescreen, cf. FIG. 5).). Note that θ is perpendicular to theabove-mentioned projection direction vector, p. This means that we candenote g(θ,s) by g(φ,s) since the latter notation more clearly indicatesthat g is a function of two variables and not a function of one scalarand one arbitrary vector. Thus, the projection value for a detectionline could be expressed as g(φ,s), i.e. as a function of the angle ofthe detection line to a reference direction, and the distance of thedetection line to an origin. We let the angle span the range 0≦φ<π, andsince the attenuation field has support in Ω_(r), it is sufficient toconsider s in the interval −r≦s≦r. The set of projections collected fordifferent angles and distances may be stacked together to form a“sinogram”.

Our goal is now to reconstruct the attenuation field a(x) given themeasured Radon transform, g=

a. The Radon transform operator is not invertible in the general sense.To be able to find a stable inverse, we need to impose restrictions onthe variations of the attenuation field.

One should note that the Radon transform is the same as theabove-mentioned projection operator in the Projection-Slice Theorem.Hence, taking the 1D Fourier transform of g(φ,s) with respect to the svariable results in central slices from the 2D Fourier transform of theattenuation field a(x).

4.3 Continuous Vs. Discrete Tomography

The foregoing sections 4.1-4.2 describe the mathematics behindtomographic reconstruction using continuous functions and operators.However, in a real world system, the measurement data represents adiscrete sampling of functions, which calls for modifications of thealgorithms. For a thorough description of such modifications, we referto the mathematical literature, e.g. “The Mathematics of ComputerizedTomography” by Natterer, and “Principles of Computerized TomographicImaging” by Kak and Slaney.

One important modification is a need for a filtering step when operatingon discretely sampled functions. The need for filtering can intuitivelybe understood by considering the Projection-Slice Theorem in a systemwith discrete sampling points and angles, i.e. a finite set of detectionlines. According to this Theorem, for each angle φ, we take the 1Ddiscrete Fourier transform of g(φ,s) with respect to the s variable andput the result into the Fourier plane as slices through the origin ofthe 2D Fourier transform of the original function a(x). This isillustrated in the left-hand part of FIG. 6 for a single projection.When we add information from several different projections, the densityof sampling points will be much higher near the origin of the 2D Fouriertransform plane. Since the information density is much higher at lowfrequencies, an unfiltered back projection will yield a blurring fromthe low frequency components.

To compensate for the non-uniform distribution of sampling points in the2D Fourier transform plane, we may increase the amount of informationabout the high spatial frequencies. This can be achieved by filtering,which can be expressed as a multiplication/weighting of the data pointsin the 2D Fourier transform plane. This is exemplified in the right-handpart of FIG. 6, where the amplitude of the high spatial frequencies areincreased and the amplitude of the low frequency components isdecreased. This multiplication in the 2D Fourier transform plane canalternatively be expressed as a convolution in the spatial domain, i.e.with respect to the s variable, using the inverse Fourier transform ofthe weighting function. The multiplication/weighting function in the 2DFourier transform plane is rotationally symmetric. Thus, we can make useof the Projection-Slice Theorem to get the corresponding 1D convolutionkernel in the projection domain, i.e. the kernel we should use on theprojections gathered at specific angles. This also means that theconvolution kernel will be the same for all projection angles.

4.4 Filtering and Back Projection

As explained in the foregoing section, the sinogram data is firstfiltered and then back-projected. The filtering can be done bymultiplication with a filter W_(b) in the Fourier domain. There are alsoefficient ways of implementing the filtering as a convolution by afilter w_(b) in the spatial domain. In one embodiment, the filtering isdone on the s parameter only, and may be described by the followingexpression:(W _(b) *f)(x)=

^(#)(w _(b)(s)*g(θ,s))≡

^(#) v,where

^(#) is a back projection operator defined as:

( # ⁢ v ) ⁢ ( x ) = 2 ⁢ ∫ 0 π ⁢ v ⁡ ( θ , x · θ ) ⁢ ⅆ φ ,

and W_(b)(x)≡

^(#)w_(b). The idea is to choose the w_(b)(s)-filter such thatW_(b)(x)≅δ(x). This is typically accomplished by working in the Fourierdomain, taking Ŵ_(b)(ξ) as a step function supported in a circular discof radius b, and letting b→∞. The corresponding filter in the spatialdomain is

${{w_{b}(s)} = {\left( \frac{b}{2\pi} \right)^{2}\left( {{\sin\;{c\left( {b\; s} \right)}} - {\frac{1}{2}\left( {\sin\;{c\left( \frac{b\; s}{2} \right)}} \right)^{2}}} \right)}},$

with continuous extension across the singularity at s=0.

In the literature, several variants of the filter can be found, e.g.Ram-Lak, Shepp-Logan, Cosine, Hann, and Hamming

5. Standard Geometries for Tomographic Processing

Tomographic processing is generally based on standard geometries. Thismeans that the mathematical algorithms presume a specific geometricarrangement of the detection lines in order to attain a desiredprecision and/or processing efficiency. The geometric arrangement may beselected to enable a definition of the projection values in a 2D samplespace, inter alia to enable the above-mentioned filtering in one of thedimensions of the sample space before the back projection.

In conventional tomography, the measurement system (i.e. the location ofthe incoupling points and/or outcoupling points) is controlled or set toyield the desired geometric arrangement of detection lines. Belowfollows a brief presentation of the two major standard geometries usedin conventional tomography e.g. in the medical field.

5.1 Parallel Geometry

The parallel geometry is exemplified in FIG. 7. Here, the systemmeasures projection values of a set of detection lines for a given angleφ_(k). In FIG. 7, the set of detection lines D are indicated by dashedarrows, and the resulting projection is represented by the functiong(φ_(k),s). The measurement system is then rotated slightly around theorigin of the x,y coordinate system in FIG. 7, to collect projectionvalues for a new set of detection lines at this new rotation angle. Asshown by the dashed arrows, all detection lines are parallel to eachother for each rotation angle. The system generally measures projectionvalues (line integrals) for angles spanning the range 0≦φ<π. When allthe projections are collected, they can be arranged side by side in adata structure to form a sinogram. The sinogram is generally given in a2D sample space defined by dimensions that uniquely assign eachprojection value to a specific detection line. In the case of a parallelgeometry, the sample space is typically defined by the angle parameter φand the distance parameter s.

Below, the use of a parallel geometry in tomographic processing isfurther exemplified in relation to a known attenuation field shown inFIG. 8A, in which the right-end bar indicates the coding of gray levelsto attenuation strength (%). FIG. 8B is a graph of the projection valuesas a function of distance s for the projection obtained at φ=π/6 in theattenuation field of FIG. 8A. FIG. 8C illustrates the sinogram formed byall projections collected from the attenuation field, where thedifferent projections are arranged as vertical sequences of values. Forreference, the projection shown in FIG. 8B is marked as a dashed line inFIG. 8C.

The filtering step, i.e. convolution, is now done with respect to the svariable, i.e. in the vertical direction in FIG. 8C. As mentioned above,there are many different filter kernels that may be used in thefiltering. FIG. 8D illustrates the central part of a discrete filterkernel w_(b) that is used in the following examples. As shown, theabsolute magnitude of the filter values quickly drop off from the centerof the kernel (k=0). In many practical implementations, it is possibleto use only the most central parts of the filter kernel, therebydecreasing the number of processing operations in the filtering step.

Since the filtering step is a convolution, it may be computationallymore efficient to perform the filtering step in the Fourier domain. Foreach column of values in the φ-s-plane, a discrete 1D Fast Fouriertransform is computed. Then, the thus-transformed values are multipliedby the 1D Fourier transform of the filter kernel. The filtered sinogramis then obtained by taking the inverse Fourier transform of the result.This technique can reduce the complexity from 0 (n²) down to0(n·log₂(n)) of the filtering step for each φ, where n is the number ofsample points (projection values) with respect to the s variable.

FIG. 8E shows the filtered sinogram that is obtained by operating thefilter kernel in FIG. 8D on the sinogram in FIG. 8C.

The next step is to apply the back projection operator. Fundamental tothe back projection operator is that a single position in theattenuation field is represented by a sine function in the sinogram.Thus, to reconstruct each individual attenuation value in theattenuation field, the back projection operator integrates the values ofthe filtered sinogram along the corresponding sine function. Toillustrate this concept, FIG. 8E shows three sine functions P1-P3 thatcorrespond to three different positions in the attenuation field of FIG.8A.

Since the location of a reconstructed attenuation value will notcoincide exactly with all of the relevant detection lines, it may benecessary to perform linear interpolation with respect to the s variablewhere the sine curve crosses between two projection values. Anotherapproach, which is less computationally effective, is to compute thefiltered values at the crossing points by applying individual filteringkernels. The interpolation is exemplified in FIG. 8F, which is anenlarged view of FIG. 8E and in which x indicates the different filteredprojection values of the filtered sinogram. The contribution to the backprojection value for the sine curve P1 from the illustrated small partof the φ-s-plane becomes:

(1 − z₂₆) ⋅ (w * g)_(26,176) + z₂₆ ⋅ (w * g)_(26,177) + (1 − z₂₇) ⋅ (w * g)_(27,175) + z₂₇ ⋅ (w * g)_(27,176) + (1 − z₂₈) ⋅ (w * g)_(28,173) + z₂₈ ⋅ (w * g)_(28,174)

The weights z_(i) in the linear interpolation is given by the normalizeddistance from the sine curve to the projection value, i.e. 0≦z_(i)<1.

FIG. 8G shows the reconstructed attenuation field that is obtained byapplying the back projection operator on the filtered sinogram in FIG.8E. It should be noted that the filtering step is important for thereconstruction to yield useful data. FIG. 8H shows the reconstructedattenuation field that is obtained when the filtering step is omitted.

5.2 Fan Geometry

Another major type of tomography arrangement is based on sampling ofdata from a single emitter, instead of measuring parallel projections atseveral different angles. This so-called fan geometry is exemplified inFIG. 9. As shown, the emitter emits rays in many directions, and sensorsare placed to measure the received energy from this single emitter on anumber of detection lines D, illustrated by dashed lines in FIG. 9.Thus, the measurement system collects projection values for a set ofdetection lines D extending from the emitter when located at angleβ_(i). In the illustrated example, each detection line D is defined bythe angular location β of the emitter with respect to a reference angle(β=0 coinciding with the x-axis), and the angle α of the detection lineD with respect to a reference line (in this example, a line going fromthe emitter through the origin). The measurement system is then rotatedslightly (δβ) around the origin of the x,y coordinate system in FIG. 9,to collect a new set of projection values for this new angular location.It should be noted that the rotation might not be limited to 0≦β<π, butcould be extended, as is well-known to the skilled person. The followingexample is given for a full rotation: 0≦β<2π.

Fan beam tomographs may be categorized as equiangular or equidistant.Equiangular systems collect information at the same angle (as seen fromthe emitter) between neighboring sensors. Equiangular systems may beconfigured with emitter and sensors placed on a circle, or the sensorsmay be non-equidistantly arranged on a line opposite to the emitter.Equidistant systems collect information at the same distance betweenneighboring sensors. Equidistant systems may be configured with sensorsplaced on a line opposite to the emitter. The following example is givenfor an equiangular system, and based on the known attenuation fieldshown in FIG. 8A. For a thorough description of the different types offan (beam) geometries, we refer to the literature.

FIG. 10A illustrates the sinogram formed by all projections collectedfrom the attenuation field in FIG. 8A, by the measurement systemoutlined in FIG. 9. In FIG. 10A, the different projections are arrangedas vertical sequences of values. It could be noted that the sinogram isgiven in a 2D sample space defined by the angular emitter locationparameter β and the angular direction parameter α.

In an exemplifying tomographic processing of the sinogram in FIG. 10A,an angle correction is first applied on all collected projectionsaccording to:g′(α_(k),β_(i))=π·(α_(k),β_(i))·cos(α_(k)).

The filtering step, i.e. convolution, is now done with respect to theα_(k) variable of the angle-corrected sinogram, i.e. corresponding tothe vertical direction in the angle-corrected sinogram. As mentionedabove, there are many different filter kernels that may be used in thefiltering. The following example uses a filter kernel similar to the oneshown in FIG. 8C. For example, many symmetric high-pass filters with acoefficient sum equal to zero may enable adequate reconstruction of theattenuation field. However, a careful choice of filter may be needed inorder to reduce reconstruction artifacts. The result may also beimproved by applying a smoothing filter in this step, as is well-knownin the art. Like in the parallel geometry, the filtering may involve aconvolution in the spatial domain or a multiplication in the Fourierdomain.

The filtered sinogram obtained by operating the filter kernel on theangle-corrected sinogram is shown in FIG. 10B.

The next step is to apply the back projection operator. The backprojection operator is different from the one used in theabove-described parallel geometry. In the fan geometry, the backprojection step may be given by the expression:

( # ⁢ v ) ⁢ ( x ) = δ ⁢ ⁢ β ⁢ ⁢ ∑ β i ⁢ 1  x - D i  2 ⁢ ( ( 1 - z ) · v ⁡ ( α k, β i ) + z · v ⁡ ( α k + 1 , β i ) ) ,

where D_(i) is the position of the source giving the β_(i) projection, zis a parameter that describes the linear interpolation between thedetection lines and a ray that extends from the source through thelocation of the respective attenuation value to be reconstructed.

FIG. 10C shows the reconstructed attenuation field that is obtained byapplying the back projection operator on the filtered sinogram in FIG.10B.

5.3 Re-Sorting Algorithms

Another approach to do the filtered back projection for a fan geometryis to choose the locations of emitters and sensors such that it ispossible to re-sort the data into a parallel geometry. Generally, suchre-sorting algorithms are designed to achieve regularly spaced datasamples in the φ-s-plane. More information about re-sorting algorithmsis e.g. found in “Principles of Computerized Tomographic Imaging” by Kakand Slaney.

To further explain the concept of re-sorting, FIG. 11 shows the datasamples (projection values) collected from two different emitters (i.e.two different values of β) in an equiangular fan beam tomograph. Thedata samples are mapped to a φ-s-plane. It can be noted that theprojection values obtained from a single emitter do not show up as astraight vertical line with respect to the s variable. It can also beseen that the φ values differ only by a constant, and that the s valuesare identical for the two different projections. One re-sorting approachis thus to collect projection values that originate from detection lineswith the same φ values (i.e. from different emitters) and let theseconstitute a column in the φ-s-plane. However, this leads to anon-uniform spacing of the s values, which may be overcome byinterpolating (re-sampling) the projection values with respect to the svariable. It should be noted that this procedure is a strictly 1Dinterpolation and that all columns undergo the same transform. It shouldalso be noted that this procedure transforms one standard tomographygeometry into another standard tomography geometry.

In order for the re-sorting algorithms to work, it is essential (asstated in the literature) that δβ=δα, i.e. the angular rotation betweentwo emitter locations is the same as the angular separation between twodetection lines. Only when this requirement is fulfilled, the projectionvalues will form columns with respect to the s variable.

6. Use of Tomographic Processing for Touch Determination

FIG. 12A illustrates the sampling points (corresponding to detectionlines, and thus to measured projection values) in the φ-s-plane for theinterleaved system shown in FIG. 2A. Due to the irregularity of thesampling points, it is difficult to apply the above-described filter.The irregularity of the sampling points also makes it difficult to applya re-sorting algorithm.

In FIG. 12A, the solid lines indicate the physical limits of the touchsurface. It can be noted that the angle φ actually spans the range from0 to 2π, since the incoupling and outcoupling points extend around theentire perimeter. However, a detection line is the same when rotated byπ, and the projection values can thus be rearranged to fall within therange of 0 to π. This rearrangement is optional; the data processing canbe done in the full range of angles with a correction of some constantsin the back projection function.

When comparing the interleaved arrangement in FIG. 2A with the fangeometry in FIG. 9, we see that the angular locations β_(i) are notequally spaced, and that angular directions α are neither equiangularnor equidistant. Also, the values attained by α are different fordifferent β_(i). The different β_(i) values for the interleavedarrangement are shown in FIG. 12B. In an ideal fan beam tomograph, thisplot would be a straight line. The step change at emitter 23 is causedby the numbering of the emitters (in this example, the emitters arenumbered counter-clockwise starting from the lower-left corner in FIG.2A). FIG. 12C exemplifies the variation in α values for emitter 10(marked with crosses) and emitter 14 (marked with circles) in FIG. 2A.In an ideal equiangular fan beam tomograph, this plot would result intwo straight lines, with a separation in the vertical direction arisingfrom the numbering of the sensors. Instead, FIG. 12C shows a lack ofregularity for both the individual emitter and between differentemitters. Another aspect is that the fan geometry assumes that thesource is positioned, for all projections, at the same distance from theorigin, which is not true for an interleaved arrangement around anon-circular touch surface.

FIG. 12D illustrates the sampling points in the φ-s-plane for thenon-interleaved system shown in FIG. 2B. Apart from the irregularity ofsampling points, there are also large portions of the φ-s-plane thatlack sampling points due to the non-interleaved arrangement ofincoupling and outcoupling points.

Thus, it is not viable to apply a filter directly on the sampling pointsmapped to a sample space such as the φ-s-plane or the β-α-plane, and thesampling points cannot be re-sorted to match any standard tomographygeometry. This problem is overcome by the re-calculation step (42 inFIG. 4A), which processes the projection values of the sampling pointsfor generation of projection values for an updated set of samplingpoints. The updated set of sampling points represent a corresponding setof fictitious detection lines. These fictitious detection lines have alocation on the touch surface that matches a standard geometry,typically the parallel geometry or the fan geometry. The generation ofprojection values of an updated set of sampling points may be achievedby interpolating the original sampling points.

The objective of the interpolation is to find an interpolation functionthat can produce interpolated values at specific interpolation points inthe sample space given a set of measured projection values at theoriginal sampling points. The interpolation points, possibly togetherwith part of the original sampling points, form the above-mentionedupdated set of sampling points. This updated set of sampling points isgenerated to be located in accordance with, for instance, the parallelgeometry or the fan geometry. The density of the updated set of samplingpoints is preferably similar to the average density of the originalsampling points in the sample space.

Many different interpolating functions can be used for this purpose,i.e. to interpolate data points on a two-dimensional grid. Input to suchan interpolation function is the original sampling points in the samplespace as well as the measured projection value for each originalsampling point. Most interpolating functions involve applying a linearoperator on the measured projection values. The coefficients in thelinear operator are given by the known locations of the originalsampling points and the interpolation points in the sample space. Thelinear operator may be pre-computed and then applied on the measuredprojection values in each sensing instance (cf. iteration of steps 40-48in FIG. 4A). Some non-limiting examples of suitable interpolationfunctions include Delaunay triangulation, and other types ofinterpolation using triangle grids, bicubic interpolation, e.g. usingspline curves or Bezier surfaces, Sinc/Lanczos filtering,nearest-neighbor interpolation, and weighted average interpolation.Alternatively, the interpolation function may be based on Fouriertransformation(s) of the measured projection values.

Below, the use of different interpolation functions in there-calculation step (step 42 in FIG. 4A) will be further exemplified.Sections 6.1 and 6.2 exemplify the use of Delaunay triangulation,section 6.3 exemplifies the use of Fourier transformation techniques,and section 6.4 exemplifies the use of weighted average interpolation.

In the examples that are based on Delaunay triangulation, the samplingpoints are placed at the corners of a mesh of non-overlapping triangles.The values of the interpolation points are linearly interpolated in thetriangles. The triangles can be computed using the well-known Delaunayalgorithm. To achieve triangles with reduced skewness, it is usuallynecessary to rescale the dimensions of the sample space (φ, s and β, α,respectively) to the essentially same length, before applying theDelaunay triangulation algorithm.

In all of the following examples, the interpolation function is able toproduce output values for any given position in the sample space.However, the frequency information in the updated set of sampling pointswill be limited according to the density of original sampling points inthe sample space. Thus, wherever the original density is high, theupdated set of sampling points can mimic high frequencies present in thesampled data. Wherever the original density is low, as well as if thereare large gaps in the sample space, the updated set will only be able toproduce low frequency variations. Non-interleaved arrangements (see FIG.2B), will produce a sample space with one or more contiguous regions(also denoted “gap regions”) that lack sampling points (see FIG. 12D).These gap regions may be left as they are, or be populated byinterpolation points, or may be handled otherwise, as will be explainedbelow in relation to a number of examples.

The following examples will illustrate re-calculation of sampling pointsinto a parallel geometry and a fan geometry, respectively. Each exampleis based on a numerical simulation, starting from a reference image thatrepresents a known attenuation field on the touch surface. Based on thisknown attenuation field, the projection values for all detection lineshave been estimated and then used in a tomographic reconstructionaccording to steps 40-46 in FIG. 4A, to produce a reconstructedattenuation field. Thus, the estimated projection values are used as“measured projection values” in the following examples.

In the examples, two different merit values are used for comparing thequality of the reconstructed attenuation fields for differentembodiments. The first merit value m₁ is defined as:

${m_{1} = \frac{\sum f}{\sum{{f - f^{\#}}}}},$

where f is a reference image (i.e. the known attenuation field) andf^(#) is the reconstructed attenuation field. The first merit valueintends to capture the similarity between the original image and thereconstructed image.

The second merit value m₁ is defined as:

${m_{2} = \frac{\sum f}{\sum\limits_{f = 0}{{f - f^{\#}}}}},$

i.e. the denominator only includes absolute differences in the regionswhere the attenuation values are zero in the reference image. The secondmerit value thus intends to capture the noise in the reconstructed imageby analyzing the regions of the image where there should be noattenuation present.

6.1 Re-Calculation into a Parallel Geometry

The following examples will separately illustrate the re-calculationinto a standard parallel geometry for an interleaved arrangement and fora non-interleaved arrangement. Since the re-calculation is made for aparallel geometry, the following examples are given for processing inthe φ-s-plane.

6.1.1 Example: Interleaved Arrangement

This example is given for the interleaved arrangement shown in FIG. 2A,assuming the reference image shown in FIG. 13. The reference image isthus formed by five touching objects 7 of different size and attenuationstrength that are distributed on the touch surface 1. For reasons ofclarity, FIG. 13 also shows the emitters 2 and sensors 3 in relation tothe reference image.

FIG. 14A is a plan view of the resulting sample space, where a mesh ofnon-overlapping triangles have been adapted to the sampling points so asto provide a two-dimensional interpolation function. FIG. 14B is aclose-up of FIG. 14A to illustrate the sampling points (stars) and theDelaunay triangulation (dotted lines extending between the samplingpoints). FIG. 14B also illustrates the interpolation points (circles).Thus, the values of the interpolation points are calculated by operatingthe Delaunay triangulation on the projection values in the samplingpoints. In the illustrated example, the interpolation points replace thesampling points in the subsequent calculations. In other words, thesinogram formed by the measured projection values is replaced by aninterpolated sinogram formed by interpolated projection values. Thereby,it is possible to obtain a uniform density of interpolation pointsacross the sample space, if desired. Each interpolation pointcorresponds to a fictitious detection line that extends across the touchsurface in accordance with a parallel geometry. Thus, the interpolationis designed to produce a set of fictitious detection lines that match aparallel geometry, that allows a reconstruction of the attenuation fieldusing standard algorithms.

As shown, the interpolation points are arranged as columns (i.e. withrespect to the s variable) in the sample space, allowing subsequent 1Dfiltering with respect to the variable. In this example, theinterpolation points are arranged with equidistant spacing with respectto the s variable, which has been found to improve the reconstructionquality and facilitate the subsequent reconstruction processing, e.g.the 1D filtering. Preferably, the inter-column distance is the same forall columns since this will make the back projection integral performbetter.

In the interpolated sinogram, each φ value with its associated s values(i.e. each column) corresponds to a set of mutually parallel(fictitious) detection lines, and thus the data is matched to a parallelgeometry in a broad sense.

FIG. 14C illustrates the interpolated sinogram, i.e. the interpolatedprojection values that has been calculated by operating theinterpolation function in FIG. 14A on the measured projection values.After filtering the interpolated sinogram with respect to the svariable, using the filter in FIG. 8D, and applying the back projectionoperator on the thus filtered sinogram, a reconstructed attenuationfield is obtained as shown in FIG. 14D, having merit values: m₁=1.3577and m₂=3.3204.

Variants for generating the updated set of sampling points are of coursepossible. For example, different interpolation techniques may be usedconcurrently on different parts of the sample space, or certain samplingpoints may be retained whereas others are replaced by interpolatedpoints in the updated set of sampling points.

As will be explained in the following, the generation of the updated setof sampling points may be designed to allow detection lines to beremoved dynamically during operation of the touch-sensitive apparatus.For example, if an emitter or a sensor starts to perform badly, or notat all, during operation of the apparatus, this may have a significantimpact on the reconstructed attenuation field. It is conceivable toprovide the apparatus with the ability of identifying faulty detectionlines, e.g. by monitoring temporal changes in output signal of the lightsensors, and specifically the individual projection signals. Thetemporal changes may e.g. show up as changes in theenergy/attenuation/transmission or the signal-to-noise ratio (SNR) ofthe projection signals. Any faulty detection line may be removed fromthe reconstruction. Such a touch-sensitive apparatus is disclosed inApplicant's U.S. provisional application No. 61/288,416, which was filedon Dec. 21, 2009 and which is incorporated herein by this reference. Tofully benefit from such functionality, the touch-sensitive apparatus maybe designed to have slightly more sensors and/or emitters than necessaryto achieve adequate performance, such that it is possible to discard asignificant amount of the projection values, for example 5%, withoutsignificantly affecting performance.

The re-calculation step (cf. step 42 in FIG. 4A) may be configured todynamically (i.e. for each individual sensing instance) account for suchfaulty detection lines by, whenever a detection line is marked asfaulty, removing the corresponding sampling point in the sample spaceand re-computing the interpolation function around that sampling point.Thereby, the density of sampling points is reduced locally (in theφ-s-plane), but the reconstruction process will continue to workadequately while discarding information from the faulty detection line.

This is further illustrated in FIGS. 15-16. FIG. 15A is a close-up oftwo-dimensional interpolation function formed as an interpolation gridin the sample space. Assume that this interpolation function is storedfor use in the re-calculation step for a complete set of samplingpoints. Also assume that the sampling point indicated by a circle inFIG. 15A corresponds to a detection line which is found to be faulty. Insuch a situation, the sampling point is removed, and the interpolationfunction is updated or recomputed based on the remaining samplingpoints. The result of this operation is shown in FIG. 15B. As shown, thechange will be local to the triangles closest to the removed samplingpoint.

If an emitter is deemed faulty, all detection lines originating fromthis emitter should be removed. This corresponds to removal of acollection of sampling points and a corresponding update of theinterpolation function. FIG. 15C illustrates the interpolation functionin FIG. 15A after such updating, and FIG. 15D illustrates the updatedinterpolation function for the complete sample space. The removal of thedetection lines results in a band of lower density (indicated by arrowL1), but the reconstruction process still works properly.

Instead, if a sensor is deemed faulty, all detection lines originatingfrom this sensor should be removed. This is done in the same way as forthe faulty emitter, and FIG. 16A illustrates the interpolation functionin FIG. 15A after such updating. FIG. 16B illustrates the updatedinterpolation function for the complete sample space. The removal of thedetection lines again results in a band of lower density (indicated byarrow L2), but the reconstruction process still works properly.

6.1.2 Example: Non-Interleaved Arrangement

The non-interleaved arrangement generally results in a different set ofsampling points than the interleaved arrangement, as seen by comparingFIG. 12A and FIG. 12D. However, there is no fundamental differencebetween the interpolation solutions for these arrangements, and allembodiments and examples of reconstruction processing described above inrelation to the interleaved arrangement are equally applicable to thenon-interleaved arrangement. The following example therefore focuses ondifferent techniques for handling the gap regions, i.e. regions withoutsampling points, which are obtained in non-interleaved arrangement.

The following example is given for the non-interleaved arrangement shownin FIG. 2B, assuming a reference image as shown in FIG. 17, i.e. thesame reference image as in FIG. 13.

FIG. 18A is a plan view of the resulting interpolation function, where amesh of non-overlapping triangles have been adapted to the samplingpoints in the sample space. Thus, this example forms the interpolationfunction directly from the original sampling points. Since the samplespace contain contiguous gap regions (see FIG. 12D), the resultinginterpolation function is undefined in these gap regions, or stateddifferently, the values at the implicit sampling points in the gapregions are set to zero. The interpolation function in FIG. 18A may beused to generate an updated set of sampling points, like in theforegoing examples. FIG. 18B illustrates the reconstructed attenuationfield that is obtained by calculating the interpolated projection valuesfor the reference image in FIG. 17, operating the 1D filter of theresult, and applying the back projection operator on the result of thefiltered data. The reconstructed attenuation field has merit values:m₁=0.7413 and m₂=1.2145.

An alternative approach to handling the gap regions is to extend theinterpolation function across the gap regions, i.e. to extend the meshof triangles over the gap regions, as shown in FIG. 19A. Theinterpolation function in FIG. 18A may thus be used to generatedesirable interpolation points within the entire sample space, i.e. alsoin the gap regions. FIG. 19B illustrates the interpolated projectionvalues calculated for the reference image in FIG. 17. It can be seenthat projection values are smeared out into the gap regions in theφ-s-plane. The reconstructed attenuation field (not shown), obtainedafter 1D filtering and back projection, has merit values: m₁=0.8694 andm₂=1.4532, i.e. slightly better than FIG. 18B.

Yet another alternative approach is to add some border vertices to theinterpolation function in the gap regions, where these border verticesform a gradual transition from the original sampling points to zerovalues, and letting the interpolation function be undefined/zero in theremainder of the gap regions. This results in a smoother transition ofthe interpolation function into the gap regions, as seen in FIG. 20A.FIG. 20B illustrates the interpolated projection values calculated forthe reference image in FIG. 17. The reconstructed attenuation field (notshown), obtained after 1D filtering and back projection, has meritvalues: m₁=0.8274 and m₂=1.4434, i.e. slightly better than FIG. 18B.

All of the three above-described approaches lead to reconstructedattenuation fields of approximately the same quality. Below follows adescription of a technique for improving the quality further, byimproving the estimation of sampling points in the gap regions.

This improved technique for generating estimation points in the gapregions will be described in relation to FIGS. 22-23. It is to be notedthat this technique may also be applied to populate gaps formed byremoval of faulty detection lines, as a supplement or alternative to thetechnique discussed in section 6.1.1. Generally, the estimation pointsmay be selected to match the standard geometries, like the interpolationpoints, possibly with a lower density than the interpolation points.FIG. 21A illustrates the sample space supplemented with such estimationpoints in the gap regions. Like in the foregoing examples, aninterpolation function is generated based on the sample space, in thiscase based on the combination of sampling points and interpolationpoints. FIG. 21B illustrates the resulting interpolation function.

The aim is to obtain a good estimate for every added estimation point.This may be achieved by making assumptions about the touching objects,although this is not strictly necessary. For example, if it can bepresumed that the touching objects are fingertips, it can be assumedthat each touching object results in a top hat profile in theattenuation field with a circular or ellipsoidal contour. Unless thenumber of touching objects is excessive, there will exist, for eachtouching object, at least one detection line that interacts with thistouching object only. If it is assumed that the touch profiles areessentially round, the touch profile will cause essentially the sameattenuation of all detection lines that are affected by the touchprofile.

The value at each estimation point, in the φ-s-plane (marked withdiamonds in FIG. 21A), represents a line integral along a specific lineon the touch surface. Since the estimation points are located in the gapregion, there is no real (physical) detection line that matches thespecific line. Thus, the specific line is a virtual line in thex-y-plane (i.e. a fictitious detection line, although it does notcorrespond to an interpolation point but to an estimation point). Thevalue at the estimation point may be obtained by analyzing selectedpoints along the virtual line in the x-y-plane. Specifically, a minimumprojection value is identified for each selected point, by identifyingminimum projection value for the ensemble of detection lines (actual orfictitious) that passes through the selected point. This means that, forevery analyzed point, the algorithm goes through the different detectionlines passing through the point and identifies the lowest value of allthese detection lines. The value of the estimation point may then begiven by the maximum value of all identified minimum projection values,i.e. for the different analyzed points, along the virtual line.

To explain this approach further, FIG. 22A illustrates the originalsampling points together with two estimation points EP1, EP2 indicatedby circles. The estimation point EP1 corresponds to a virtual line V1,which is indicated in the reference image of FIG. 22B. The next step isto evaluate selected points along the virtual line V1. For everyselected point, the projection values for all intersecting detectionlines are collected. The result is shown in the two-dimensional plot ofFIG. 22C, which illustrates projection values as a function of detectionline (represented by its angle) and the selected points (given asposition along the virtual line). The large black areas in FIG. 22Ccorrespond to non-existing detection lines. To find the value of theestimation point EP1, the data in FIG. 22C is first processed toidentify the minimum projection value (over the angles) for eachselected point along the virtual line V1. The result is shown in thegraph of FIG. 22D. The value of the estimation point EP1 is thenselected as the maximum of these minimum projection values. FIG. 22Eillustrates the values of all estimation points in FIG. 21A calculatedfor the reference image in FIG. 17 using this approach, together withthe interpolated projection values. By comparing FIG. 19B and FIG. 20B,a significant improvement is seen with respect to the information in thegap regions of the sample space. The reconstructed attenuation field,obtained after 1D filtering and back projection, is shown in FIG. 22Fand has merit values: m₁=1.2085 and m₂=2.5997, i.e. much better thanFIG. 18B.

It is possible to improve the estimation process further. Instead ofchoosing the maximum among the minimum projection values, the processmay identify the presence of plural touch profiles along theinvestigated virtual line and combine (sum, weighted sum, etc) themaximum projection values of the different touch profiles. To explainthis approach further, consider the estimation point EP2 in FIG. 22A.The estimation point EP2 corresponds to a virtual line V2, which isindicated in the reference image of FIG. 23A Like in the foregoingexample, selected points along the virtual line V2 are evaluated. Theresult is shown in the two-dimensional plot of FIG. 23B. Like in theforegoing example, the data in FIG. 23B is then processed to identifythe minimum projection value (over the angles) for each selected pointalong the virtual line V2. The result is shown in the graph of FIG. 23C.This graph clearly indicates that there are two separate touch profileson the virtual line V2. Thus, the estimation process processes themaximum projection values in FIG. 23C to identify local maxima (in thisexample two maxima), and sets the value of the estimation point EP2equal to the sum of the local maxima (projection values). FIG. 23Dillustrates the values of all estimation points in FIG. 21A calculatedfor the reference image in FIG. 17 using this approach, together withthe interpolated projection values. The gap regions of the sample spaceare represented by relevant information. The reconstructed attenuationfield, obtained after 1D filtering and back projection, is shown in FIG.23E and has merit values: m₁=1.2469 and m₂=2.6589, i.e. slightly betterthan FIG. 22F.

FIG. 24 is a flowchart of an exemplifying reconstruction process, whichis a more detailed version of the general process in FIG. 4A adapted fordata processing in a touch-sensitive apparatus with a non-interleavedarrangement. The process operates on the output signal from the lightsensor arrangement, using data stored in a system memory 50, andintermediate data generated during the process. It is realized that theintermediate data also may be stored temporarily in the system memory 50during the process. The flowchart will not be described in great detail,since the different steps have already been explained above.

In step 500, the process samples the output signal from the light sensorarrangement. In step 502, the sampled data is processed for calculationof projection values (g). In step 504, the process reads theinterpolation function (IF) from the memory 50. The interpolationfunction (IF) could, e.g., be designed as any one of the interpolationfunctions shown in FIGS. 18A, 19A, 20A and 21B. The process also reads“exclusion data” from the memory 50, or obtains this data directly froma dedicated process. The exclusion data identifies any faulty detectionlines that should be excluded in the reconstruction process. The processmodifies the interpolation function (IF) based on the exclusion data,resulting in an updated interpolation function (IF′) which may be storedin the memory 50 for use during subsequent iterations. Based on theupdated interpolation function (IF′), and the projection values (g),step 504 generates new projection values (“interpolation values”, i) atgiven interpolation points. Step 504 may also involve a calculation ofnew projection values (“estimation values”, e) at given estimationpoints in the gap regions, based on the updated interpolation function(IF′). Step 504 results in a matched sinogram (g′), which contains theinterpolation values and the estimation values. In step 506, the processreads the filter kernel (w_(b)) from the memory 50 and operates thekernel in one dimension on the matched sinogram (g′). The result of step506 is a filtered sinogram (o). In step 508, the process reads “subareadata” from the memory 50, or obtains this data directly from a dedicatedprocess. The subarea data indicates the parts of the attenuationfield/touch surface to be reconstructed. Based on the subarea data, andthe filtered sinogram (u), step 510 generates a reconstructedattenuation field (a), which is output, stored in memory 50, orprocessed further. Following step 508, the process returns to step 500.

It is to be understood that a similar process may be applied for dataprocessing in a touch-sensitive apparatus with an interleavedarrangement.

6.2 Re-Calculation into Fan Geometry

The following example will illustrate the re-calculation into a standardfan geometry for an interleaved arrangement. Since the re-calculation ismade for a fan geometry, the following examples are given for theβ-α-plane.

6.2.1 Example: Interleaved Arrangement

This example is given for the interleaved arrangement shown in FIG. 2A,assuming a reference image as shown in FIG. 13.

A first implementation of the re-calculation step (cf. step 42 in FIG.4A) will be described with reference to FIG. 25. In the firstimplementation, the sampled data is “squeezed” to fit a specific fangeometry. This means that the projection values obtained for thedetection lines of the interleaved arrangement are re-assigned tofictitious detection lines that match a fan geometry, in this examplethe geometry of an equiangular fan beam tomograph. Making such are-assignment may involve a step of finding the best guess for anequiangular spacing of the β_(i) values, and for the α_(k) values. Inthis example, the β_(i) values for the sampling points arere-interpreted to be consistent with the angles of an equiangular fanbeam tomograph. This essentially means that the difference in rotationangle between the different incoupling points is considered to be thesame around the perimeter of the touch surface, i.e. δβ=2·π/M, where Mis the total number of emitters (incoupling points). The α_(k) valuesfor the sampling points are re-interpreted by postulating that the α_(k)values are found at n·δα, where −≦n≦N and 2N+1 is the total number ofsensors (outcoupling points) that receive light energy from the relevantemitter. To get accurate ordering of the α_(k) values, n=0 may be set asthe original sample with the smallest value of α_(k).

FIG. 25A illustrates the sampling points in the β-α-plane, after thisbasic re-assignment of projection values. After angle correction, 1Dfiltering of the angle-corrected data, and back projection, areconstructed attenuation field is obtained as shown in FIG. 25B. It isevident that the first implementation is able to reproduce the originalimage (FIG. 13), but with a rather low quality, especially in the cornerregions.

In a second implementation of the re-calculation step, the measuredprojection values are processed for calculation of new (updated)projection values for fictitious detection lines that match a fangeometry. In the second implementation, like in the firstimplementation, each emitter (incoupling point) on the perimeter of thetouch surface is regarded as the origin of a set of detection lines ofdifferent directions. This means that every β_(i) value corresponds toan emitter (incoupling point) in the interleaved arrangement, whichgenerates a plurality of detection lines with individual angulardirections α_(k), and the sampling points defined by the actual β_(i)values and α_(k) values thus form columns in the β-α-plane. Therefore,interpolation in the β_(i) direction can be omitted, and possibly bereplaced by a step of adding an individual weighting factor to the backprojection operator (by changing δβ to δβ_(i), which should correspondto the difference in β_(i) values between neighboring emitters). In thesecond implementation, the re-calculation step involves an interpolationwith respect to the α_(k) variable, suitably to provide values ofinterpolation points having an equidistant separation with respect tothe α_(k) variable for each β_(i) value in the sampling space. Thus, theinterpolation of the sampling points may be reduced to applying a 1Dinterpolation function. The 1D interpolation function may be of anytype, such as linear, cubic, spline, Lanczos, Sinc, etc. In followingexample, the interpolation function is linear. It should be noted,though, that a 2D interpolating function as described in section 6.1above can alternatively be applied for interpolation in the β-α-plane.

FIG. 26A illustrates the sampling points in the β-α-plane, after the 1Dinterpolation. FIG. 26B shows the reconstructed attenuation field whichis obtained after angle correction, 1D filtering of the angle-correcteddata, and back projection. By comparing FIG. 26B with FIG. 25B, it canbe seen that the second implementation provides a significant qualityimprovement compared to the first implementation.

Further, by comparing FIG. 26B with FIG. 14D, which both illustratereconstructed attenuation fields for the interleaved arrangement, it mayappear as if the parallel geometry may result in a higher reconstructionquality than the fan geometry. This apparent quality difference may haveseveral causes. First, reconstruction algorithms for the fan geometryrestrict the direction angle α to the range −π/2≦α≦π/2. Direction anglesoutside this range will cause the angle correction (see section 5.2) todeteriorate. In the touch-sensitive apparatus, detection lines may havedirection angles outside this range, especially for emitters located thecorners of the touch surface (recalling that α=0 for a line going fromthe emitter through the origin, i.e. the center of the touch surface).Second, the weighted back projection operator (see section 5.2) involvesa normalization based on the inverse of the squared distance between thesource and the reconstructed position. This distance becomes close tozero near the perimeter of the touch surface and its inverse goestowards infinity, thereby reducing the reconstruction quality at theperimeter. Still further, the standard reconstruction algorithms assumethat all sensors (outcoupling points) are arranged at the same distancefrom the emitters (incoupling points).

A third implementation of the re-calculation step will now be describedwith reference to FIGS. 27-28. In the third implementation, which isdesigned to at least partially overcome the above-mentioned limitationsof the first and second implementations, the detection lines are definedbased on fictive emitter/sensor locations. FIG. 27 illustrates thetouch-sensitive apparatus circumscribed by a circle C which may or maynot be centered at the origin of the x,y coordinate system (FIG. 2) ofthe apparatus. The emitters 2 and sensors 3 provide a set of detectionlines (not shown) across the touch surface 1. To define the detectionlines in a β-α-plane, the intersection of each detection line and thecircle C is taken to define a β_(i) value, whereas the α_(k) value ofeach detection line is given by the inclination angle of the detectionline with respect to a reference line (like in the other fan geometryexamples given herein). Thereby, the β and α variables are defined instrict alignment with the theoretical definition depicted in FIG. 9,where the β variable is defined as a rotation angle along a circularperimeter.

FIG. 28A illustrates the resulting sampling points in the β-α-plane forthe interleaved system shown in FIG. 27, where the β_(i) values aredefined according to the foregoing “fictive circle approach”. Thesampling space contains a highly irregular pattern of sampling points.FIG. 28B is a plan view of a 2D interpolation function fitted to thesampling points in FIG. 28A. It should be realized that the techniquesdescribed in sections 6.1.1 and 6.1.2 may be applied also to thesampling points in the β-α-plane to generate interpolation/estimationpoints that represent fictitious detection lines matching a standard fangeometry. Thus, the interpolation/estimation points are suitablygenerated to form columns with respect to the β variable, preferablywith equidistant spacing. FIG. 28C illustrates the interpolatedsinogram, which is obtained by operating the interpolation function inFIG. 28B on the projection values that are given by the reference imagein FIG. 13. FIG. 28D shows the reconstructed attenuation field which isobtained after angle correction, 1D filtering of the angle-correcteddata, and back projection. By comparing FIG. 28D with FIG. 26B, it canbe seen that the third implementation provides a significant qualityimprovement compared to the first and second implementations.

In all of the above implementations, the re-calculation step results inan updated sinogram, in which each β value and its associated α values(i.e. each column in the sinogram) corresponds to a fan of detectionlines with a common origin, and thus the data is matched to a fangeometry in a broad sense.

6.3 Re-Calculation by Fourier Transformation

In tomography theory, it is generally assumed that g(φ, s) is bandwidthlimited. Thereby, it is possible to use Fourier transformationalgorithms to perform the re-calculation step (step 42 in FIG. 4A) so asto form the above-mentioned updated set of sampling points.

There is a class of Fourier transformation algorithms that are designedto enable Fourier transformation of irregularly sampled data. Thesealgorithms may e.g. involve interpolation and oversampling of theoriginal data, e.g. using least-squares, iterative solutions or Fourierexpansion (Shannon's sampling theorem). This type of Fouriertransformation algorithm comes in many different names and flavors, e.g.Non-Uniform FFT (NUFFT/NFFT), Generalized FFT (GFFT), Non-uniform DFT(NDFT), Non-Equispaced Result FFT (NER), Non-Equispaced Data FFT (NED),and Unequally spaced FFT (USFFT).

In the following, a brief example is given on the use of the NEDalgorithm in a re-calculation step into a standard parallel geometry.The theory behind the NED algorithm is further described in the article“Non-Equispaced Fast Fourier Transforms with Applications to Tomography”by K Fourmont, published in “Journal of Fourier Analysis andApplications”, Volume 9, Number 5, pages 431-450 (2003), which isincorporated herein by this reference.

The example involves two FFT operations on the original set ofprojection values in the sinogram g(φ,s). First, a two-dimensional NEDFFT algorithm is operated on the sinogram:

g ^ ⁡ ( ϑ , σ ) ⁢ ← ⁢ g ⁡ ( φ k , s k ) ,

whereby the Fourier transform of the sinogram is computed. As notedabove, the NED algorithm is designed to process irregularly sampleddata, and the resulting Fourier coefficients (∂,σ) will be arranged in aCartesian grid. Then, a regular two-dimensional inverse FFT algorithm isoperated on the Fourier coefficients to get an updated set of projectionvalues arranged in a standard geometry, in this example a parallelgeometry:

g ⁡ ( φ , s ) ⁢ ← ⁢ g ^ ⁡ ( ϑ , σ ) .

A regular inverse FFT algorithm can be used since both the input dataĝ(ν,σ) and the output data g(φ,s) are arranged on a Cartesian grid.

In this example, it may be advantageous for the c·N-periodicity of there-calculation step to be for φ=2π. This may be achieved by mirroringthe sinogram values before applying the NED FFT algorithm:g(φ,s)=g(φ−π,−s) for π≦φ<2π. However, this extension of the sinogram isnot strictly necessary. In a variant, it is merely ensured that thewrapping behavior of the c·N-periodicity is consistent with themirroring of the sinogram values.

It can be noted that the above example is equally applicable forre-calculation into a fan geometry, by changing (φ,s) to (α,β)

It is also to be understood that the re-calculation is not limited tothe use of the NED FFT algorithm, but can be achieved by applying anyother suitable Fourier transformation algorithm designed for irregularlysampled data, e.g. as listed above.

6.4 Re-Calculation by Weighted Average Interpolation

The interpolation in the re-calculation step (step 42 in FIG. 4A) may bebased on a weighted average algorithm. Like Delaunay triangulation, theweighted average algorithm involves applying a linear operator on themeasured projection values, with the coefficients in the linear operatorbeing given by the known locations of the original sampling points andthe interpolation points in the sample space.

One benefit of weighted average interpolation is that the computation ofthe coefficients may be simple to implement, e.g. compared to Delaunaytriangulation. Another benefit is the possibility of doing on-the-flycomputation of the coefficients in the linear operator (instead of usingpre-computed coefficients) if available memory is limited, e.g. when thesignal processor (10 in FIG. 1) is implemented as an FPGA.

These benefits will be further illustrated by way of an example, inwhich a weighted average algorithm is used for on-the-fly interpolationof original projection values g(φ_(k),s_(k)) into a matched sinogramg′(φ_(i)′,s_(j)′), in three steps S1-S3. Reverting to FIG. 14B, theoriginal projection values correspond to the sampling points (stars),and the matched sinogram corresponds to the interpolation points(circles). In the following example, the weight function is representedas F_(WF):

-   -   S1. Initialize an accumulator sinogram, acc(φ_(i)′,s_(j)′), and        a weight sinogram, w(φ_(i)′,s_(j)′), by setting them to zero.    -   S2. For each sampling point (φ_(k),s_(k)), execute the following        sequence of sub-steps i.-iii. for all interpolation points        (φ_(i)′,s_(j)′):        -   i. φ=F_(WF)(Δφ,Δs)=F_(WF)(φ_(k)−φ_(i)′,s_(k)−s_(j)′)        -   ii. acc(φ_(i)′,s_(j)′)=acc(φ_(i)′,s_(j)′)+ω·g(φ_(k),s_(k))        -   iii. w(φ_(i)′,s_(j)′)=w(φ_(i)′,s_(j)′)+ω    -   S3. For each interpolation point (ω_(i)′,s_(j)′), compute the        matched sinogram:        -   If w(φ_(i)′,s_(j)′)>0, then set            g′(φ_(i)′,s_(j)′)=acc(φ_(i)′,s_(j)′)/w(φ_(i)′,s_(j)′),            otherwise set g′(φ_(i)′,s_(j)′)=0

There are numerous weight functions F_(WF) that may be used in this andother examples. One characteristic of a suitable weight function F_(WF)is that it decreases as |Δφ|, |Δs| increase. The constants in the weightfunction F_(WF) may be chosen such that each projection valueg(φ_(k),s_(k)) contributes to only one or a few interpolation points(φ_(i)′,s_(j)′). This makes it possible to speed up the interpolationsignificantly since step S2 is reduced to an accumulation in thevicinity of the respective sampling point (φ_(k),s_(k)). In one example,the sub-steps i.-iii. are only executed for the 3×3 interpolation points(φ_(i)′,s_(j)′) that are closest to each sampling point (φ_(k),s_(k)) inthe sample space.

A few non-limiting examples of weight functions include:F_(WF)(Δφ,Δs)=e^(−(Δφ) ² ^(/2σis φ) ² ^(+Δs) ² ^(/2σ) ^(s) ²⁾ , andF_(WF)(Δφ,Δs)=1/(1+α₁·Δφ²+α₂·Δs²), where σ_(φ), σ_(s), α₁, α₂ areconstants.

Generally, the interpolation by weighted average may be seen to involve,for each interpolation point, a step of calculating a weightedcontribution to the value of the interpolation point from at least asubset of the sampling points (e g implemented by S2: i.-ii.), and astep of aggregating the weighted contributions (e g implemented by S2:iii. and S3), wherein each weighted contribution is calculated as afunction of the projection value of the sampling point and a distance inthe sample space between the interpolation point and the sampling point.

It can be noted that the above discussion is equally applicable forre-calculation into a fan geometry, by changing (φ,s) to (α,β).

7. Alternative Reconstruction Techniques in Standard Geometries

It is to be understood that the reference to Filtered Back Projection(FBP) herein is merely given as an example of a technique forreconstructing the attenuation field. There are many other knowntechniques that can be used for reconstruction, after re-calculationinto a standard geometry, such as for instance ART, SIRT, SART andFourier-transform based algorithms. More information about these andother algorithms can be found, e.g., in the above-mentioned books “TheMathematics of Computerized Tomography” by Natterer, and “Principles ofComputerized Tomographic Imaging” by Kak and Slaney.

It should also be noted that it is possible to do an unfiltered backprojection and perform the filtering on the reconstructed image.

Fourier-transform based algorithms give the promise of time complexitiesof O(n²·log(n)), i.e. a significant improvement. However, as stated byKak and Slaney, the naïve algorithm may not suffice. The naïve algorithmis discussed by Natterer on pages 119-125, whereupon Natterer continuesto present two different improved algorithms (on pages 125-127) that arestated to produce good results. The above-referenced article by Fourmontpresents further algorithms that involve the use of FFT-based algorithmsdesigned to handle uneven distribution of input data and/or output data.

It can also be noted that in certain implementations, it may beadvantageous to perform a low-pass filtering of the updated set ofprojection values that results from the re-calculation into a standardgeometry, before applying the reconstruction technique.

8. Concluding Remarks

The invention has mainly been described above with reference to a fewembodiments. However, as is readily appreciated by a person skilled inthe art, other embodiments than the ones disclosed above are equallypossible within the scope and spirit of the invention, which is definedand limited only by the appended patent claims.

For example, the reconstructed attenuation field may be subjected topost-processing before the touch data extraction (step 48 in FIG. 4A).Such post-processing may involve different types of filtering, for noiseremoval and/or image enhancement. FIG. 29 illustrates the result ofapplying a Bayesian image enhancer to the reconstructed attenuationfield in FIG. 23E. The enhanced attenuation field has merit values:m₁=1.6433 and m₂=5.5233. For comparison, the enhanced attenuation fieldobtained by applying the Bayesian image enhancer on the reconstructedattenuation field in FIG. 14D has merit values: m₁=1.8536 andm₂=10.0283. In both cases, a significant quality improvement isobtained.

Furthermore, it is to be understood that the inventive concept isapplicable to any touch-sensitive apparatus that defines a fixed set ofdetection lines and operates by processing measured projection valuesfor the detection lines according to any tomographic reconstructionalgorithm that is defined for a standard geometry, where these standardgeometry does not match the fixed set of detection lines. Thus, althoughthe above description is given with reference to FBP algorithms, theinventive concept have a more general applicability.

It should also be emphasized that all the above embodiments, examples,variants and alternatives given with respect to interpolation, removalof detection lines, and estimation in gap regions are generallyapplicable to any type of emitter-sensor arrangement and irrespective ofstandard geometry.

Furthermore, the reconstructed attenuation field need not represent thedistribution of attenuation coefficient values within the touch surface,but could instead represent the distribution of energy, relativetransmission, or any other relevant entity derivable by processing ofprojection values given by the output signal of the sensors. Thus, theprojection values may represent measured energy, differential energy(e.g. given by a measured energy value subtracted by a background energyvalue for each detection line), relative attenuation, relativetransmission, a logarithmic attenuation, a logarithmic transmission,etc. The person skilled in the art realizes that there are other ways ofgenerating projection values based on the output signal. For example,each individual projection signal included in the output signal may besubjected to a high-pass filtering in the time domain, whereby thethus-filtered projection signals represent background-compensated energyand can be sampled for generation of projection values.

Furthermore, all the above embodiments, examples, variants andalternatives given with respect to an FTIR system are equally applicableto a touch-sensitive apparatus that operates by transmission of otherenergy than light. In one example, the touch surface may be implementedas an electrically conductive panel, the emitters and sensors may beelectrodes that couple electric currents into and out of the panel, andthe output signal may be indicative of the resistance/impedance of thepanel on the individual detection lines. In another example, the touchsurface may include a material acting as a dielectric, the emitters andsensors may be electrodes, and the output signal may be indicative ofthe capacitance of the panel on the individual detection lines. In yetanother example, the touch surface may include a material acting as avibration conducting medium, the emitters may be vibration generators(e.g. acoustic or piezoelectric transducers), and the sensors may bevibration sensors (e.g. acoustic or piezoelectric sensors).

Still further, the inventive concept may be applied to improvetomographic reconstruction in any field of technology, such asradiology, archaeology, biology, geophysics, oceanography, materialsscience, astrophysics, etc, whenever the detection lines are mismatchedto a standard geometry that forms the basis for the tomographicreconstruction algorithm. Thus, the inventive concept could be generallydefined as a method for image reconstruction based on an output signalfrom a tomograph, the tomograph comprising a plurality of peripheralentry points and a plurality of peripheral withdrawal points, whichbetween them define actual detection lines that extend across ameasurement space to propagate energy signals from the entry points tothe withdrawal points, at least one signal generator coupled to theentry points to generate the energy signals, and at least one signaldetector coupled to the withdrawal points to generate the output signal,the method comprising: processing the output signal to generate a set ofdata samples, wherein the data samples are indicative of detected energyfor at least a subset of the actual detection lines; processing the setof data samples to generate a set of matched samples, wherein thematched samples are indicative of estimated detected energy forfictitious detection lines that have a location in the measurement spacethat matches a standard geometry for tomographic reconstruction; andprocessing the set of matched samples by tomographic reconstruction togenerate data indicative of a distribution of an energy-relatedparameter within at least part of the measurement space.

The invention claimed is:
 1. A method of enabling touch determinationbased on an output signal from a touch-sensitive apparatus, thetouch-sensitive apparatus including a panel, a plurality of peripherallight emitters and a plurality of peripheral light detectors, theplurality of peripheral light emitters configured to transmit lightsignals to the plurality of peripheral light detectors, the transmittedlight signals defining actual detection lines across a surface portionof the panel between pairs of light emitters and light detectors, thetouch-sensitive apparatus further including at least one signalgenerator coupled to the plurality of peripheral light emitters togenerate the light signals, wherein the plurality of peripheral lightdetectors are configured to generate the output signal, the methodcomprising: processing the output signal to generate a set of datasamples in a two-dimensional sample space, wherein each data sample isrepresentative of an actual detection line, and wherein the data samplesare defined by a signal value indicative of detected energy for at leasta subset of the actual detection lines and two dimensional values thatdefine the location of the actual detection line on the surface portion;processing the set of data samples to generate a set of matched samplesat locations in the two-dimensional sample space, each matched samplesamples having an estimated signal value, wherein the matched samplesare indicative of estimated detected energy for fictitious detectionlines that have a location on the surface portion that matches astandard geometry for tomographic reconstruction, the processing the setof data samples including, calculating the estimated signal valuesaccording to a two-dimensional interpolation function and based on thesignal values of the data samples; and processing the set of matchedsamples by tomographic reconstruction to generate data indicative of adistribution of an energy-related parameter within at least part of thesurface portion.
 2. The method of claim 1, wherein the locations in thetwo-dimensional sample space correspond to the fictitious detectionlines.
 3. The method of claim 1, wherein each estimated signal value iscalculated by interpolation of the signal values of neighboring datasamples in the two-dimensional sample space.
 4. The method of claim 1,wherein the processing the set of data samples further comprises:obtaining the two-dimensional interpolation function, thetwo-dimensional interpolation function having nodes corresponding to theset of data samples.
 5. The method of claim 1, further comprising:receiving exclusion data identifying one or more of the data samples tobe excluded; and wherein the processing the set of data samples furtherincludes, identifying a node corresponding to each of the one or moredata samples to be excluded, re-designing the two-dimensionalinterpolation function without the identified one or more nodes, andcalculating the estimated signal values according to the re-designedinterpolation function and based on the signal values of the datasamples corresponding to the nodes of the re-designed interpolationfunction.
 6. The method of claim 1, wherein the calculating theestimated signal values includes, for each matched sample, calculating aweighted contribution to the matched sample from each of at least asubset of the data samples, and aggregating the weighted contributions;and each weighted contribution is calculated as a function of the signalvalue of the data sample and a distance in the two-dimensional samplespace between the matched sample and the data sample.
 7. The method ofclaim 1, wherein the matched samples are arranged as at least one ofrows and columns in the two-dimensional sample space.
 8. The method ofclaim 7, wherein the matched samples are arranged with equidistantspacing within each of said at least one of rows and columns.
 9. Themethod of claim 1, wherein the processing the set of data samplesfurther comprises: operating a two-dimensional Fourier transformationalgorithm designed for irregularly sampled data on the set of datasamples to generate a set of Fourier coefficients arranged in aCartesian grid; and calculating the estimated signal values by operatinga two-dimensional inverse Fourier transformation algorithm on the set ofFourier coefficients to generate the set of matched samples.
 10. Themethod of claim 1, wherein the processing the set of matched samplescomprises: applying one-dimensional high-pass filtering of the matchedsamples in the two-dimensional sample space to generate filteredsamples; and processing the filtered samples to generate a set of backprojection values indicative of said distribution.
 11. The method ofclaim 1, wherein the surface portion of the panel defines a samplingarea in the two-dimensional sample space; and if the actual detectionlines given by a geometric arrangement of the plurality of peripherallight emitters and the plurality of peripheral light detectors result inat least one contiguous region without data samples within the samplingarea, the processing the set of data samples includes obtaining a set ofestimated sampling points within the at least one contiguous region, andfor each estimated sampling point, identifying the location of acorresponding fictitious detection line on the surface portion,identifying, for each intersection point between the correspondingfictitious detection line and the actual detection lines or between thecorresponding fictitious detection line and the fictitious detectionlines for the set of matched samples, an intersection point value as asmallest signal value of all data samples corresponding to the actualdetection lines associated with the intersection point, and calculatinga signal value of the estimated sampling point as a function of theintersection point values.
 12. The method of claim 11, wherein thesignal value of the estimated sampling point is given by the largestintersection point value.
 13. The method of claim 11, furthercomprising, for each estimated sampling point: identifying a number oflocal maxima in the intersection point values; and calculating thesignal value of the estimated sampling point as a combination of thelocal maxima.
 14. The method of claim 1, wherein the two-dimensionalvalues include a rotation angle of the actual detection line in theplane of the panel, and a distance of the actual detection line in theplane of the panel from an origin.
 15. The method of claim 1, whereinthe two-dimensional values include an angular location of a lightemitter or light detector corresponding to the actual detection line,and a rotation angle of the actual detection line in the plane of thepanel.
 16. The method of claim 15, wherein the standard geometry is afan geometry; the touch surface has a non-circular perimeter; and theangular location is defined by an intersection between the actualdetection line and a fictitious circle arranged to circumscribe thetouch surface.
 17. The method of claim 1, wherein the standard geometryis one of a parallel geometry and a fan geometry.
 18. The method ofclaim 1, wherein the panel defines a touch surface and an oppositesurface; said at least one signal generator is arranged to provide lightinside the panel such that the light propagates from the plurality ofperipheral light emitters by internal reflection between the touchsurface and the opposite surface to the plurality of peripheral lightdetectors for detection by said at least one signal detector; and thetouch-sensitive apparatus is configured such that the propagating lightis locally attenuated by one or more objects touching the touch surface.19. A non-transitory computer-readable medium comprising computer codewhich, when executed on a data-processing system, causes thedata-processing system to carry out the method of claim
 1. 20. Themethod of claim 1, wherein a geometry of the actual detection linesassociated with each of the plurality of peripheral light emitters isdefined by angles between each of the actual detection lines associatedwith a corresponding peripheral light emitter, and a length of each ofthe actual detection lines associated with the corresponding peripherallight emitter.
 21. The method of claim 1, wherein geometries of actualdetection lines associated with at least a portion of the plurality ofperipheral light emitters are different.
 22. The method of claim 1,further comprising: detecting at least one touch interaction with thepanel based on the generated data.
 23. A device for enabling touchdetermination based on an output signal of a touch-sensitive apparatus,said touch-sensitive apparatus including a panel, a plurality ofperipheral light emitters and a plurality of peripheral light detectors,the plurality of peripheral light emitters configured to transmit lightsignals to the plurality of peripheral light detectors, the transmittedlight signals defining actual detection lines that extend across asurface portion of the panel between pairs of light emitters and lightdetectors, the touch-sensitive apparatus further including means forgenerating the light signals at the plurality of peripheral lightemitters, and the plurality of peripheral light detectors generating theoutput signal, said device comprising: means for processing the outputsignal to generate a set of data samples in a two-dimensional samplespace, wherein each data sample is representative of an actual detectionline, and wherein the data samples are defined by a signal valueindicative of detected energy for at least a subset of the actualdetection lines and two dimensional values that define a location of theactual detection line on the surface portion; means for processing theset of data samples to generate a set of matched samples at locations inthe two-dimensional sample space, each matched sample having anestimated signal value, wherein the matched samples are indicative ofestimated detected energy for fictitious detection lines that have alocation on the surface portion that matches a standard geometry fortomographic reconstruction, the means for processing the set of datasamples including, means for calculating the estimated signal valuesaccording to a two-dimensional interpolation function and based on thesignal values of the data samples; and means for processing the set ofmatched samples by tomographic reconstruction to generate dataindicative of a distribution of an energy-related parameter within atleast part of the surface portion.
 24. A touch-sensitive apparatus,comprising: the device for enabling touch determination according toclaim 23; the panel; the plurality of peripheral light emittersconfigured to transmit the light signals to the plurality of peripherallight detectors; the means for generating the light signals at theplurality of peripheral light emitters; the plurality of peripherallight detectors generating the output signal.
 25. The device of claim23, further comprising: means for detecting at least one touchinteraction with the panel based on the generated data.
 26. Atouch-sensitive apparatus, comprising: a panel; a plurality of lightemitters and a plurality of light detectors arranged at the periphery ofthe panel, wherein the plurality of light emitters are configured totransmit light signals to the plurality of light detectors to defineactual detection lines that extend across a surface portion of the panelbetween pairs of the plurality of light emitters and the plurality oflight detectors, and wherein the plurality of light detectors areconfigured to generate an output signal based on the transmitted lightsignals; at least one signal generator coupled to the plurality of lightemitters to generate the light signals; and a signal processorconfigured to process the output signal to generate a set of datasamples in a two-dimensional sample space, wherein each data sample isrepresentative of an actual detection line, and wherein the data samplesare defined by a signal value indicative of detected energy for at leasta subset of the actual detection lines and two dimensional values thatdefine a location of the actual detection line on the surface portion,process the set of data samples to generate a set of matched samples atlocations in the two-dimensional sample space, each matched samplehaving an estimated signal value, wherein the matched samples areindicative of estimated detected energy for fictitious detection linesthat have a location on the surface portion that matches a standardgeometry for tomographic reconstruction, and wherein the estimatedsignal values are calculated according to a two-dimensionalinterpolation function and based on the signal values of the datasamples, and process the set of matched samples by tomographicreconstruction to generate data indicative of a distribution of anenergy-related parameter within at least part of the surface portion.27. The touch-sensitive apparatus of claim 26, wherein the signalprocessor is further configured to detect at least one touch interactionwith the panel based on the generated data.